The asylum seeker child at the centre of a 10-day protest in Brisbane will be returned to Nauru, Immigration Minister Peter Dutton says.

Baby Asha has been transferred from Lady Cilento Children's Hospital to community detention, after being treated by doctors who refused to discharge the one-year-old back into offshore detention.

Mr Dutton today confirmed the child had been moved into community detention, where an officer will remain with the family.

He told the ABC the Government would stick to its policy of returning asylum seekers to offshore detention once medical and legal issues had been resolved.

"People will go back to Nauru," he said.

"In the interim, we will make an assessment case by case as to whether or not it's safe for the family to live in the community."

Mr Dutton said Queensland Police were investigating the matter, stating "if we say there are security issues, domestic violence issues or there are claims of criminal activity, then in that case we will make a decision that the person does not leave the detention centre".

Opposition Leader Bill Shorten said the safety of the asylum seeker child "had to be paramount".

When asked about the issue today, Mr Shorten reiterated Labor's support for offshore processing, but highlighted the need for independent oversight of centres.

"The Government must deal with the unacceptable, indefinite detention which is occurring to some of the people on Nauru and Manus," he said.

"They must take up Labor's policies of proper oversight.

"I respect that Papua New Guinea and Nauru are sovereign nations, but these people are indirectly in Australia's care, so we need to make sure they get the highest standard of care."

Dutton closes door on New Zealand resettlement offer

Mr Dutton also appeared to close the door on an offer from New Zealand to resettle some of the group of 267 asylum seekers currently in Australia.

The group, which includes more than 30 babies, could be sent back to Nauru after the High Court threw out a challenge to the Government's offshore detention network earlier this month.

New Zealand Prime Minister John Key said last week it was "potentially possible" for New Zealand to take in some of the asylum seekers, citing an agreement made with the former Gillard government in 2013.

But Mr Dutton described it as a failed proposal.

"The deal that was struck was a back-door option to come to Australia," he said.

"It was a failed proposal under Julia Gillard and that is why it is not acceptable to us in the form that Julia Gillard brokered it."