Tamil parents Priya and Nades Murugappan and their Australian-born daughters Tharnicaa, 3, and Kopika, 6, have been in detention since 2018, and on Christmas Island since August 2019.

Tharnicaa and her mother were evacuated from the island to Perth earlier this week, and the three-year-old is now being treated at Perth Children's Hospital.

Grandmothers Against Detention of Refugee Children's Bendigo convenor Di O'Neil said the community had long been concerned about the family's welfare in detention.

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"I have been very concerned about this family for a number of years now," she said.

"I think regardless of what led to the fact that Tharnicaa has been flown to Perth over the past week, it does seem to be that maybe the border forces have been a bit slow in seeking the care that she needed.

"It's really exasperating."

Ms O'Neil said this was just another situation where the children experienced health concerns.

"In the 12 months in detention in Melbourne, both children had developed and suffered from a Vitamin D deficiency," she said.

"Tharnicaa has also had a number of teeth removed when she was very young because she didn't have the correct diet.

"This is now one more medical punishment that the family is going through."

Australia's home affairs department has denied mistreating the youngest daughter of the Biloela family detained on Christmas Island, whose potentially deadly blood infection has been linked to untreated pneumonia.

Tharnicaa's mother said her daughter was sick for almost two weeks and that 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 released on Tuesday.

"I hope that Tharnicaa can get the help she needs now. Please, help us to get her out of detention and home to Biloela."

Family supporter Angela Fredericks said Tharnicaa suffered dangerous temperature spikes on the journey to Perth and had since been diagnosed with a blood infection resulting from untreated pneumonia.

The Department of Home Affairs and Australian Border Force said Tharnicaa had been receiving medical treatment and daily monitoring on Christmas Island consistent with medical advice.

Ms O'Neil believed the family was being used by the federal government as a "first line of defence to stop the boats".

She said the Bendigo community would continue to support the family and rally for its release.

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"People in the community just can't believe people can be so nasty as Australians to this little family of four," she said.

"They are two Australian-born girls whose parents were very well accepted in the town they lived in."

Priya and Nades settled in the Queensland town of Biloela after arriving separately by boat from Sri Lanka.

Sisters Tharnicaa Kopika were born in Australia.

The federal government has vowed to never permanently resettle anyone who arrived illegally by boat, and does not consider the girls to be Australian citizens.

The family has been in detention since 2018, and on Christmas Island since August 2019.

- with AAP

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