The federal government will not send a two-week-old baby and his asylum-seeker family from Brisbane to Nauru before next week after lawyers sought a court order to stop their removal.

A spokeswoman at law firm Maurice Blackburn said the government had given an undertaking not to remove the family until further order of the court.

"We expect this matter will be back in court on Tuesday morning," she said.

Associate Murray Watt said the family from Myanmar had already been "mistreated", with restrictions placed on the family's ability to visit the baby boy in hospital after his birth in Brisbane two weeks ago.

Mr Watt said they were terrified they could be taken to Nauru at any time, even though the baby remains weak, has trouble breastfeeding and his mother is recovering from a Caesarean birth and suffers from diabetes.