The family has been granted a three-month extension of their current visa until early July, according to family friend David Randall who started the change.org petition calling on Immigration Minister David Coleman to reconsider their deportation. The petition has now been signed by more than 50,000 people.

"The minister says he requires more medical reports to consider the decision about whether or not he should intervene, but my gut feeling is they wanted out of the media for the election. I mean both sides of politics would do that," Mr Randall said.

"Their case was getting a fair bit of media attention and there was more coming."

There could be a new immigration minister after the May 18 federal election but the office of Opposition immigration spokesman Shayne Neumann has previously said Labor supports the current immigration laws.

The Wangchuk family has lived in Australia since 2012. The boys attend Queanbeyan High School and the parents work in child care and aged care in Canberra.

The family's application for permanent residency was rejected because their son Kinley, who is deaf, did not meet the health requirements set out by immigration laws.

The requirement assesses whether someone's condition is likely to result in "significant costs to the Australian community or prejudice the access of Australian citizens and permanent residents to services in short supply".

Unions ACT is coordinating a crowd-funding campaign to help the family pay for independent medical assessments of their son to present to the government, to complement whatever tests that are ordered by the Commonwealth medical officer.

Mr Randall said the medical tests would cost around $15,000, money the family just does not have, with any of their savings put into the legal fees and migration agent.

Unions ACT secretary Lyndal Ryan said they money would go direct to the family.

The fundraising was being done via helpkinley.raisely.com/ with more than $2000 raised so far.

"They've been advised it would be good to have a specialist assessment done, independent of [the Commonwealth medical officer]," Ms Ryan said.

"This could be very valuable to the family and help Kinley into the future.

"If the people of Canberra and the region could make a donation, that would be terrific."

Meanwhile, Mr Randall said whoever was the new immigration minister post-May 18 would be faced with a compelling argument to allow the family to stay in Australia.

He said 18-year-old Kinley was in "perfect health" and unlikely to cause a drain on government funding into the future.

"His hearing aids and hearing testing can be catered for through Better Hearing Australia, which has offered to provide that for at least five years," Mr Randall said.

"Other than that, he's a perfectly healthy young man who happens to have a hearing loss and some learning difficulties. He doesn't have behaviour problems. He would cope quite well in an assisted work placement.

"The family can look after his long-term needs if they're allowed to stay and continue working. He is certainly no drain on the Australian community."

Kinley's mother Jangchu is a childcare worker at the Nipperville Early Learning Centre in Watson. His dad Tshering is an aged-care worker at the Jindalee Aged Care Residence in Narrabundah as well as a cleaner in ACT schools.

Their supporters say they are a hard-working family who just want to secure their sons' futures in Australia.

"The minister potentially could make a politically safe decision because it's a win-win," Mr Randall said.

"His parents moved to a regional area, they're working in difficult-to-fill areas of aged care and early education and they're both highly-qualified for those roles.

"Dad was an surgical nurse back in Bhutan and mum was paediatric nurse back in Bhutan. They're exceedingly well-qualified."