It's just one of many double-take touches intended to capsize traditional ways of thinking – and cruising – on this seven-night voyage from Miami to the Dominican Republic, the inaugural cruise of Carnival's newest line, Fathom.

Fathom is not just the new kid on the block, it's a very different kind of kid.

"We don't think of it as a cruise. For us, we're like the new beverage that's delivered in the same bottle," says Fathom president Tara Russell, an engineer with a passion for "business with purpose" and more than a decade of hands-on experience setting up not-for-profits in Thailand and the US.

Two years ago Russell approached Carnival Corporation, the largest travel company in the world, with a new concept in cruising. "Social impact travel" brings together travellers who want to make a difference and gives them the resources to do that.

Just don't call it voluntourism. One of our "impact guides" goes so far as to say that's a "cuss word", playing on the perception that voluntouring prioritises the needs of travellers instead of the people they're trying to help. Fathom, by contrast, is community-driven, working closely with two established NGOs in the Dominican Republic. But there's another important difference.

"Social impact travel combines a lot of the elements of voluntourism," concedes Russell, "but we do believe it's a different approach in the sense that we have a volume and scale that is unmatched."

So instead of sending a few, or a few dozen, volunteers to a destination a few times a year, an entire ship full of them will be visiting the Dominican Republic every second week throughout the year, and for years to come. (On alternate weeks, Fathom offers "cultural immersion" cruises to neighbouring Cuba, which started in May this year.)

But before we can do good in the DR, we have to get there. One of the reasons this is Fathom's first social impact destination, apart from the fact that 40 per cent of Dominicans live below the poverty line, is that it's less than two sea-days from Miami, making it ideal for a one-week cruise: two days cruising there, three days in port, two days back.

As a non-cruiser, I hadn't been especially looking forward to those first two days at sea. I'd seen this cruise as a means to an end, not an end in itself – until I experience how different Fathom's way of cruising is.

We're on a relatively small ship, for one thing: the 704-berth, former P&O vessel MV Adonia, refurbished by Fathom earlier this year. It's also liberally sprinkled with thoughtful, whimsical Fathom touches, from "messages in bottles" bobbing in the pool (for us to write notes to future Fathom travellers) and a curtained video booth (to record our impressions of the cruise) to the "Note to future self" wall (where we write postcards to ourselves about this moment, which Fathom mails for us) and Curiosity Boxes containing thought-provoking quotes scattered around the ship.

And while the Adonia retains some of its Britishness (think: fox-hunting paintings in one bar and velvet armchairs that clash with the Caribbean climate), its more traditional spaces have been Fathom-ed too (the name is meant to convey depth and understanding).

The library is a book-lover's delight, filled with titles curated to inspire and open minds, and there's an on-board book club. Everything in the ship's shops supports a cause, from Stop the Water While Using Me organic cosmetics to WeWood recycled wooden watches and Krochet Kids clothing with labels signed by the women who made them. There's a bar, the Glass House, that serves only organic wines; a focus on sustainable produce in the restaurants; and Ocean Grill, formerly run by Marco Pierre White, is now the domain of Dominican celebrity chef Emil Vega.

There's even a Fathom app to help you navigate the extensive menu of on-board activities, which are the surprise highlight of the cruise for me.

Some of the workshops are practical, preparing us for the DR with English-teaching tips and Spanish-speaking lessons. Others are designed to go deeper, as Fathom's design director Ryan Fiorentino explains: "This is about our ability to journey into the world, spark new ideas, redefine problems, start conversations between people and create something bigger than the ship."

At first it's as if we're being indoctrinated into the "cult" of Fathom with sessions such as Being a Fathom Traveller featuring rejigged inspirational quotes ("Life begins at the start of your discomfort zone") and evangelically energetic impact guides using made-up words such as "alongsideness", "architecting" and "solutioning" ("not probleming").

But that feeling soon fades, allowing us to concentrate on the task at hand: stretching our minds with brainstorms, storytelling circles and improv-like exercises about, say, using business ideas to solve environmental problems. My favourite is the curiosity workshop created by San Francisco design firm Curiosity Atlas, whose clients have included Google and Facebook, partly because sitting in a room full of other question-askers makes me feel as if I've found my tribe.

All week, in fact, I keep meeting like-minded people, which fosters a collegiate atmosphere. The size of the ship helps; it's small enough that you start seeing familiar faces after a day or two, big enough that you're still meeting new people at dinner on the last night. We're also united by the fact that most of us are non-cruisers. (Even Russell; when I confess to her that this is my first cruise, she says, "Mine too!") This is no accident; these trips are designed to appeal to people who don't choose to cruise, specifically values-driven Millennials, families seeking meaningful and educational vacations (children must be over eight, the minimum age for Fathom's volunteering activities) and empty-nesters with the time and resources to give back.

Stimulating as shipboard life has been, it's exciting to arrive at Amber Cove at lunchtime on day three, even if Carnival's new $US83 million port on the north coast of the DR does jolt us back to cruiseland. As we walk through the duty-free store, past the resort-style pool area with its bars and battalions of sun lounges and into a pastel-coloured Truman Show-like village (designed to mimic the Victorian-era buildings in nearby Puerto Plata), Fathom suddenly seems like a goldfish in a very big pond.

But this is just a portal we have to pass through to reach the real reason we're here: to spend three days doing some hands-on volunteering.

Three "impact activities" are included in the cost of the cruise, but there are seven in total and you can do as many as you like. You can teach English to 4th and 5th graders or join a "community English" lesson for adults in their homes. You can make clay water filters (more than three million Dominicans don't have access to clean water) or improve the health of a family by replacing the dirt floor of their house with a concrete one.

I join a reforestation group to plant native palms and help at two women's co-operatives: one that makes chocolate (where we help sort cacao seeds, pour chocolate into moulds and wrap chocolate bars) and one that recycles paper, cleaning up the environment as well as producing hand-made paper for sale.

It's at the Repapel paper-making centre that I see first-hand how impact can be a two-way street. We're only there for a morning, but the women's warmth and joyful attitude is infectious; while showing us how to make paper from pulp, for instance, they sing La Bamba and do a hip-bumping dance that has us all laughing together. It's the tiniest window into their lives, but they seem genuinely happy to have us there and when it's time to go and they wrap us in sisterly hugs, we're all wiping tears from our eyes.

You could be forgiven for wondering how much good anyone can do in a few hours. I wonder that too, until I see the outcomes of our cruise. During our three-day visit, my fellow Fathom travellers and I taught English to 636 people (363 children and 273 adults), planted 2408 trees, wrapped 6320 chocolate bars, made 584 sheets of recycled paper and 50 water filters (giving 50 homes access to clean water) and concreted the floors of two houses (improving the quality of life for 20 people).

Multiply these impacts by a year and add a few larger ships (guests on Carnival's nine other brands can now do impact activities during their stopovers in Amber Cove) – this is social impact in action. "This year we've got almost half a million travellers coming to the DR," says Russell. "So you think about how many trees we planted this week, with just a fraction of those travellers. Imagine the number of water filters we could produce…"

The two-day cruise back to Miami is a chance to wind down, but the on-board program rolls on, taking a different tack. Instead of preparing us for the DR, there are workshops to help us integrate what we've learned, seen and felt into our lives and communities back home.

One afternoon, walking back to my cabin, I'm drawn into Anderson's Bar by a soulful voice and an acoustic guitar and suddenly I'm not on a ship in the Caribbean any more; I could be in a jazz bar in Melbourne or Manhattan. That's when it hits me. Imagine a bunch of hip, young things taking over a ship, putting up inspirational billboards urging us to #traveldeep, infusing everything with innovative and ethical ideas and taking travellers to destinations in need. That's this cruise in a nutshell.

Fathom hasn't converted me to cruising, much as I love the whole "unpacking once" thing and the convenience and comfort of spending a week on a ship. But that was never the plan. Fathom's mission is bigger than growing the cruise market: to do nothing less than change the world, one tree, one cruise and one well-intentioned traveller at a time.

DIVE INTO THE CULTURE

Play dominoes in the street, dance the meringue, listen to "bachata" music or go to a baseball game (a national obsession).

TRIP NOTES

MORE INFORMATION

godominicanrepublic.com

GETTING THERE

Qantas flies daily to Miami from Sydney via LAX, San Francisco or Dallas and from Melbourne via LAX; see qantas.com

CRUISING THERE

Fathom's seven-night cruises depart from Miami every second Sunday throughout the year. All-inclusive inaugural season fares start at $US499 per person ($US599 for an outside cabin) plus taxes for sailings before November 20, 2016. See fathom.org

Louise Southerden travelled as a guest of Fathom.

Four more things to do in the DR

HAVE AN ADVENTURE

Fathom's shore excursions include snorkelling, catamaran sailing and a 27-waterfall day trip. Or swim with humpback whales, January-April; see aquaticadventures.com

EXPLORE PUERTO PLATA

"Silver Port" (named by Columbus in 1493 because it shimmered in the sun) has a fort, an amber museum and charming colonial buildings.

GET HIGH

Ride the cable car to the top of Isabel de Torres for its botanical garden, Dominican restaurant and mini Christ the Redeemer statue.

TAKE A ROAD TRIP

Rent a car and driver and head east for lunch or sundowners at the popular surfing and kitesurfing town of Cabarete.