Aborigines, who own part of the popular tourist resort island, said they would file an injunction with the nation's highest court to stop the cull, which has also met with opposition from some environmentalists.
A lawyer for the Ngulungbara people, Sherrill O'Connor, said they had given the authorities until noon on Friday to end the killings.
But the premier for Queensland state said that while he respected the "passionate" views of environmentalists and Aborigines, the action would continue.
"I know there is criticism of our decision to cull - I would simply state that a young boy has died," he was quoting as saying in the Sydney Morning Herald.
"We take no pleasure in this but we have a duty of care to residents and visitors."
'Illogical' move
Federal Environment Minister Robert Hill said it was illogical of the state government to order a cull before the results of a risk assessment study currently being conducted on the dingoes.
He said while safety was important, he did not want to see dingoes killed unnecessarily.
He added that the Queensland government had stalled on a draft plan for two years on dingo management.
Large packs
Jan Oliver, president of the Queensland Wildlife Preservation Society, said constant feeding by tourists had allowed large packs of male dogs, that would not normally survive, to thrive on the island.
"The alpha female - the dominant dog - is now less in control," she said.
Mr Beattie has ordered a strict $500 on-the-spot fine for feeding the animals.
Conservationists are split on whether the dingoes need to be culled - some argue that the present population can only be sustained by dingoes scavenging food from tourists.
Eric Parups, president of the Fraser Island Association called for eradication all of the dogs.
"It's us or them and with the many, many millions of dollars that the tourist industry brings it would be hard for the government to say 'Let's leave the dogs'," he said.
The 160 dingoes, considered the purest strain of dingoes in Australia, are protected by law.