An asylum seeker facing imminent deportation from Australia, which would separate her from her 18-month-old baby, has been given a temporary reprieve, with the United Nations now investigating her case.

Huyen Tran sought asylum in Australia by boat with her brother in 2011, saying she faced religious persecution in Vietnam because she is Catholic, a religious minority there. Tran was placed in community detention in Australia, but an assessment determined she was not entitled to protection. In 2015, after her friends in community detention were deported, Tran grew fearful of the same fate and fled.

Before authorities found her and moved her to the Melbourne Immigration Transit Accommodation detention centre in 2017, Tran met and married her partner, Paul, and became pregnant. She gave birth to her daughter, Isabella, while in detention and they have remained there ever since. Tran is not permitted to live in the community with Paul, who lives in Australia on a 457 working visa and is unable to sponsor his wife.

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Her lawyers argue she has not been fairly assessed.

On 4 November Tran was told she would be deported any time from 25 November. Tran feared being immediately detained upon returning to Vietnam, making it too dangerous to take Isabella with her.

The notice prompted Tran’s lawyer, Alison Battisson, to lodge a complaint with the United Nations Human Rights Committee, which confirmed it was investigating the case. Battisson claims Tran and Isabella have been subject to human rights breaches including their right to a private life and the right for a child not to be separated from family.

The committee responded by saying it had asked the Australian government not to deport Tran while it considered her case. It also asked the government to “take all necessary measures to prevent physical or psychological or irreparable harm to Ms Tran and [Isabella], having particular regard to [Isabella’s] needs as a child”. The committee said a copy of the request had been delivered to the government.

On Wednesday night, Battisson said Tran’s case manager had confirmed that Tran’s deportation had been put on hold while it conducted its own investigation.

“Obviously we welcome the government making an inquiry into potential human rights breaches in separating a mother from their child,” Battisson told Guardian Australia.

“This is a toddler who has been in the care of her mother for her entire life and who knows no other carer. However, I don’t think it takes significant legal analysis to figure out separating families, particularly a mother and toddler, breaches many international conventions Australia has signed up to.”

Battisson said the uncertainty around Tran and Isabella’s future had taken its toll on the family.

“They are very stressed and concerned about their futures together,” she said.

“There is some concern about whether Isabella is meeting milestones in a detention centre environment. Detention centres are not designed for children and cannot be made sufficiently safe or engaging for children especially at very delicate developmental milestones. It will continue to be a fraught and stressed existence for them.”

In January, Tran said she was being denied appropriate food for Isabella and in July she was treated for flu.

Huyen has been regularly visited by journalist Rebekah Holt throughout her time in detention. She told Holt on Wednesday night that she remained fearful for her future.

“I hope this means something good but I am still so worried they will send me away from my baby and husband,” Huyen said.

“I don’t really understand what the government means when they say they will investigate separately from the UN but I hope they explain it to my lawyer in a letter so I can read it.

“We could be at home with my husband who can support us, I don’t know why they won’t put me on my husband’s visa, we aren’t criminals and why are they putting us through this when I have been in Australia so long?”