The family, whose case rests on the two-year-old and her right to apply for a protection visa, now cannot be deported by the Australian government until the matter is decided through the court system.
A date has not yet been set for their case to be heard.
Priya and Nades Murugappan and daughters Tharunicaa, two, and Kopika, four, had previously settled in the Queensland township of Biloela.
They were being deported in August, under instruction by the federal government, when their flight was ordered to land due to a late-night court injunction.
The family has since been detained in "jail-like" conditions on Christmas Island.
Tharunicaa, despite being Australian-born, would normally also be refused refugee status due to legislation blocking children of asylum seekers who arrive by boat from accessing the nation's protection.
But the Federal Court was told earlier this week that Tharunicaa was legally entitled to apply for a protection visa during a short period in 2017 when her mother's visa application was not yet finalised, following a determination by Home Affairs Minister Peter Dutton.
An application was made for Tharunicaa last week, but barrister Stephen Lloyd, acting for the federal government, argued on Wednesday the window of opportunity had closed.
The family were granted a 24-hour lifeline by the Federal Court on Wednesday after the hearing failed to reach a resolution in the high-profile case.
Barrister Angel Aleksov, acting for the family, argued Tharunicaa's visa application was "still in train", meaning the government did not have the power to forcibly remove the child and her family until her case was decided.
Mr Dutton earlier expressed his frustration that the case was dragging on, labelling it "infuriating", particularly due to the costs to Australian taxpayers.
What happens next to the Biloela family?
The Sri Lankan family will remain in legal limbo on Christmas Island with their bid to stay in Australia hinging on an upcoming court trial. So, what’s next for the Tamil family?
WHO ARE THE TAMIL FAMILY?
Husband and wife Nadesalingam and Priya Murugappan and their daughters Kopika, four, and Tharunicaa, two.
WHEN DID THEY COME TO AUSTRALIA?
Nadesalingam and Priya arrived from Sri Lanka separately by boat in 2012 and 2013.
WHEN WERE THEY FIRST REMOVED FROM BILOELA?
In March 2018, immigration officials came to the family's home in Biloela, Queensland, and took them to a Melbourne detention centre.
WHY ARE THEY BEING DEPORTED?
Priya's bridging visa has run out. Previous cases involving claims for refugee status made on behalf of Kopika and the parents have failed.
WHAT HAPPENS NEXT?
A Federal Court trial will be scheduled, with a judge or panel to decide the legality of Tharunicaa's bid for a protection visa.
No date has been set. A family lawyer said it could be months away. Supporters want them brought back to Biloela until the trial ends.
WHAT HAPPENED AT EARLIER HEARINGS?
Federal Court judge Mordy Bromberg on Thursday made an order blocking the government from deporting the family until a visa fight for Tharunicaa is determined at trial.
The youngest daughter had never been assessed for a protection visa and the federal government argued she was not entitled to one. But family lawyers objected, citing previous changes to legislation.
In late August, the family was being deported when a Federal Court judge granted a last-minute injunction forcing a plane en-route to Sri Lanka to land in Darwin.
The family was moved from Darwin to Christmas Island.
Subsequent injunctions meant the family has remained on Christmas Island and they are expected to remain there until the trial is finalised.
WHAT'S BEEN SAID?
Prime Minister Scott Morrison said he would not intervene because it would send the wrong message to other people seeking asylum.
Opposition Leader Anthony Albanese called on the government to let the family stay, labelling the saga "publicly funded cruelty".
Home Affairs Minister Peter Dutton says he thinks the Tamil parents are being "unfair" to their own children by pursuing a legal case destined for "failure".