A three-year-old asylum seeker being treated for a blood infection at a Perth hospital could be sent back to detention on Christmas Island within days, family supporters say.
Tharnicaa is receiving care at Perth Children's Hospital after being evacuated from the island with her mother Priya Murugappan earlier this week.
Her potentially deadly blood infection has been linked by supporters to untreated pneumonia.
The Home to Bilo group on Wednesday said Tharnicaa's temperature had improved and Priya was reporting her to be "brighter and better" but still not eating.
"Doctors are awaiting results from blood taken yesterday for tests, which will take two days to come back," the group said in a statement.
"Pending those results, Priya believes that she and Tharni could be sent back to Christmas Island by the end of this week, possibly as early as Friday. There has been no indication from Australian Border Force if this will be the case."
The Tamil family has been on Christmas Island, far off the West Australian coast, for two years after being removed from their home in Biloela, Queensland.
They have pleaded to be allowed to remain in Australia.
Federal authorities have been threatening to send them back to Sri Lanka, despite the family's fears they would be targeted.
The Murugappan family's lawyer Carina Ford on Wednesday said they had had no communication with the federal government about the prospect of being sent to the US or New Zealand, amid suggestions they were likely destinations.
"For the record we and our clients have not been approached about this by the government - we have written to the Department of Home Affairs to ask why," Ms Ford tweeted.
On Tuesday, Home Affairs Minister Karen Andrews said "a range of resettlement options" were under negotiation.
Foreign Minister Marise Payne later expanded on that statement, saying the US and NZ were options.
"I do know that the Minister for Home Affairs, Ms Andrews, has indicated that there are two options there and the United States and New Zealand are both in the frame," she told Sydney radio 2GB.
The family has an ongoing court proceeding related to their case, which would normally preclude any sudden change in their resettlement status.
Supporters of the family will hold candlelight vigils outside Perth Children's Hospital on Wednesday evening and at Sydney Town Hall on Thursday.
Priya said her daughter was sick for almost two weeks and medical contractors at the immigration detention centre repeatedly refused to take her to hospital.
"I want to thank everybody for their love and good wishes," Priya said in a video message as she cradled her daughter.
"I hope that Tharnicaa can get the help she needs now. Please, help us to get her out of detention and home to Biloela."
Contractor IHMS said in a statement to AAP the child had received "appropriate and timely medical care" but declined to answer specific questions about her care for privacy reasons.
"IHMS and its employees take the health and welfare of all our clients very seriously and work tirelessly to support all those in our care."
Home Affairs and Australian Border Force said Tharnicaa had been receiving medical treatment and daily monitoring on Christmas Island consistent with medical advice.
"As soon as the ABF was advised by the treating medical practitioners that the minor required medical treatment in Western Australia, the minor was transferred to a hospital in Western Australia," an official said.
"The Australian Border Force strongly denies any allegations of inaction or mistreatment of individuals in its care."
Healthcare for detainees was "broadly comparable" with that on the mainland, the government has said.
Priya, her husband Nades and their Australian-born daughters Tharnicaa and Kopika, 6, have been in detention since 2018, and on Christmas Island since August 2019.
The government has previously vowed to never permanently resettle anyone who arrives illegally by boat.