Councillor Dennis Seage put forward a question without notice to the business meeting last week, asking for Daisy to be part of an educational program, encouraging residents to buy branded milk.

He heard supermarkets were stocking Victorian milk and thought the council should be using every resource to support its industries.

"A, she's a dairy cow, and B, she's a little tourist icon and she's really good at building cultural awareness. It would make sense to involve Daisy, and I'm sure she'd agree."

He said he wanted to involve community groups and schools in the final design if the council were to support the proposal.

Councillor Andrew Sloan also put forward a question to ask Woolworths why two-litre bottles of Dairy Farmers Original Milk were no longer available at the Kiama store. Jamberoo dairy farmers supply to the brand and had their excess milk price slashed in July.

"They stock the one-litre bottles because there's demand from the elderly buyers, but I'm a father of three young kids and we go through a lot of milk," Cr Sloan said.

He questioned whether Woolworths had intentionally priced Dairy Farmers out of the market because he had seen the brand priced cheaper at corner shops.

A Woolworths spokeswoman did not respond to questions on competitive pricing, but said the two-litre range had been pulled from the store for more than a year.

"Woolworths always looks to support local suppliers," she said.

"In the Kiama store we made the decision to range a local branded milk, South Coast Milk, which is sourced from [Shoalhaven] dairy farmers as opposed to a national brand.

"Woolworths is committed to supporting the dairy industry by working with suppliers on a long-term sustainability basis."

A report will be made on both matters.