A High Court ruling earlier this month validated the nation's off-shore detention regime and paved the way for who came to Australia for health reasons, and Australian-born babies, to be deported back to Nauru.
Human Rights Law Centre director of legal advocacy Daniel Webb said authorities had previously promised to give these people 72 hours warning before sending them to Nauru, but was now seeking to fast-track their deportation.
"The government looks like it is clearing the way for fast-track deportations by removing basic notice periods," he said on Tuesday.
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Mr Webb said the asylum-seeker families involved were terrified they would be woken in the night and returned to the remote Pacific island nation.
It was a matter of basic fairness and due process that these people have the chance to speak with their lawyers before being deported, he said.
While many others face the possibility of being deported without warning, the government had agreed to give baby Asha and her parents 72 hours notice before being sent back to Nauru.
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But that happened only after an emergency High Court application was filed on the family's behalf, Mr Webb said.
Twelve-month-old Asha remains in the Lady Cilento Children's Hospital in Brisbane after being admitted last month for treatment for accidental burns from boiling water in detention on Nauru.
She has since recovered but is being held by medical staff until "a suitable home environment is identified".
While Immigration Minister Peter Dutton has been tight-lipped, his predecessor Scott Morrison has said the government will continue to hold its line, "absolutely, completely".
Queensland's premier and health minister have supported the doctors involved and protesters have maintained a vigil - as well as daily rallies - outside the hospital.
Opposition Leader Lawrence Springborg said patients who were well and healthy should be discharged.
There have also been daily rallies around the country, including outside the Royal Prince Alfred hospital in Sydney.
