Supporters of the Biloela Tamil family are calling for the parents and two daughters to be released from detention on Christmas Island while they wait for their case to be resolved.
Priya and Nades Murugappan and daughters Tharunicaa, two, and Kopika, four, are facing months in "isolation" on Christmas Island after a federal court judge ruled on Thursday that a full hearing is needed to consider the two-year-old daughter's case.
The three other family members have already been refused refugee status.
While supporters are celebrating Thursday's court decision, they are increasingly concerned about the conditions on Christmas Island.
Asked whether they would request a move, lawyer for the family, Carina Ford, said it was up to the Home Affairs Department or minister to decide where the family were held while they waited.

An earlier photo of the detained Tamil family from Biloela. Source: Supplied
"It can take months, it could be a while yet," Ms Ford said outside the Federal Court in Melbourne.
"They are at Christmas Island, it is isolating, they haven't had any children to play with. Given they're the only ones there I think it's self-explanatory how I feel about that issue."
The family were living in the Queensland town of Biloela up until March 2018 when they were taken into detention in Melbourne ahead of their planned deportation.
Last month, Australian Border Force officers placed the family on a plane bound for Sri Lanka, but a last-minute injunction issued mid-flight forced the plane to land in Darwin.
They were then taken to Christmas Island, with Home Affairs Minister Peter Dutton citing concerns for the safety of officers due to potential demonstrations.
Biloela resident and family friend Angela Fredericks called on Mr Dutton to move the family back to mainland Australia.
"We’re very concerned about their wellbeing over there, so we’re very much are calling for them to be placed, if not in (the) community, back in detention in Australia where we know they can have visitors, they’ve got access to the internet and we can ensure they are connected to the community," Ms Fredericks told SBS News.

Priya's friend Angela Fredericks wants the prime minister to intervene to block the family's deportation. Source: SBS News
Ms Fredericks was particularly worried about four-year-old Kopika.
"Kopika hasn’t seen any children for weeks now, she’s incredibly lonely and she hates it.
"Eighteen months in detention is long enough, she doesn’t need any more isolation."
Mr Dutton insists the family is living in a house on Christmas Island and is free to move around and go to the nearby pool or school.
Ms Fredericks, who visited the family earlier this month, rejected his description, saying the family's social interaction was limited to security guards.
"I’ve been over there myself, I had to have permission to go in, I got searched, I wasn’t allowed to take anything in."