A Dublin couple who emigrated to Australia a decade ago could be deported because their application for permanent residency could mean taxpayers there may have to pay for their son's cystic fibrosis treatment.

Anthony Hyde, who works as a part-time bus driver in Seymour, Victoria, and his wife Christine who is an assistant principal at a primary school there, emigrated to Australia in 2009.

They are living there with their son Darragh, three, who was born there in 2015, less than three weeks after they applied for permanent residency.

During their application, which they began after they met the criteria for a skilled visa, Darragh was diagnosed with cystic fibrosis in medical tests which were carried out as part of the process.

However, in October 2015 the Australian Department of Home Affairs rejected their application because Darragh’s condition could mean the need for a lung transplant in the future, which would cost the taxpayer.

They are due to appeal the decision at the Administrative Review Tribunal on April 30, saying their son's medication, Kalydeco, is covered under the Pharmaceutical Benefits Scheme (PBS).

Ms Hyde told Australia's 9News: "It's made a huge difference. He has never had any hospital admissions and he doesn't go to the doctors any more or less than any other three-year-old."

However, he was still seen as a "burden" due to his reliance on medication.

They are relying on Australia's Immigration Minister, David Coleman, to reverse the deportation order with Ms Hyde saying: "This is it for us. The minister is the only person who can help.

“We don’t want to go back to Ireland. There is nothing there for us."

They have set up a petition, which has more than 8,000 signatures, asking for support to overturn their deportation

They said: "Darragh has been doing extremely well considering his condition, and we have positive letters from his doctors and specialist stating that he should live a full life and that his disease progression will be much slower than average.

His condition has no effect on his cognitive ability and should he wish to finish school and go to University, he has every chance at being successful in a career path of his choosing. Darragh is a bright boy with a positive future ahead of him.

"We have always felt extremely grateful to live in Australia. I studied here gaining my Masters in Special Education. I have worked full-time as a school teacher and now as an Acting Assistant Principal and my husband works part-time as a bus driver. We have been living in Australia for almost 10 years and have a strong support network here with our friends and family and we are well settled in regional Victoria.

Darragh has the support of his family, our large support network in Seymour and the wider Australian community."

A spokesperson from Australia's Department of Home Affairs said: "For certain visas, primary criteria for the grant of the visa requires that all members of a family unit satisfy certain requirements.

"If one of the members of a family unit does not satisfy these requirements, then the primary applicant will not meet the criteria for the grant of the visa."