Three members of the Biloela Tamil family have been given bridging visas for three months, which will allow the parents work and study rights.
Immigration Minister Alex Hawke has granted the visas to Nades and Priya Murugappan and their elder daughter Kopika.
The status of the younger daughter Tharunicaa - whose illness and transfer from Christmas Island for medical care led to the government relocating the family to live in Perth - is unchanged, and she remains in "community detention".
While she is now out of hospital Tharunicaa is to have medical treatment for some time.
The family will still be prevented from moving from Perth.
Tharunicaa's status is the subject of a complicated legal battle as the Murugappans fight against deportation.
The government's determination that the family should go back to Sri Lanka is on the grounds the parents have been found not to be refugees.
The family will continue to have access to government-provided housing, health care, schooling and support services.
If all four were on bridging visas they would not be entitled to the house they are now living in.
The family applied for the bridging visas last week, and the deadline for Hawke to make a decision came this week.
The timing coincided with Barnaby Joyce's elevation to Nationals leader and Deputy Prime Minister. Joyce has spoken strongly for the family being allowed to go back to Biloela. But government sources said Joyce had had no influence on the visa decision.
Author: Michelle Grattan - Professorial Fellow, University of Canberra