Jonny and Julie Gordon, whose eight-year-old daughter Kate suffers from the disease, provided two of more than 16,000 signatures on a petition that has been lodged with the Scottish Parliament.
The couple, from Giffnock in East Renfrewshire, who both work in accident and emergency, want the life-saving drug Kalydeco, also known as ivacaftor, to be introduced in Scotland as soon as possible.
The drug is currently under consideration by the Scottish Medicines Consortium (SMC) and Mr Gordon claims his family could be forced to leave the country and seek the drug elsewhere if the decision is negative.
The treatment was approved for use by NHS boards in England on December 19 and is already in use in the US and some European countries.
It is the first drug of its kind to treat the cause of a certain strain of the disease rather than just the symptoms.
Patients who have used the drug have reported remarkable results, with some whose only hope of recovery was a lung transplant reported to be leading active lives just weeks after starting treatment.
Mr Gordon, who works at Glasgow's Victoria Infirmary, said: "We have spent many years looking into treatment for Kate and Kalydeco is the only thing that has come close to a cure – it effectively pauses the disease.
"It's a breakthrough drug. Nothing in the last few years has come close to the results it has had, even outwith CF, and it's so frustrating not to be in a position to get that for our child. Working in hospitals, Julie and I also see a number of children suffering from the disease and really struggling and it's hard to deal with it when you know there is something out there that could really help them."
He added: "If it comes to it, we will move to another country, to the US if we have to, to get Kate the treatment she needs.
"As a parent, years down the line, we need to be able to say we've done everything we can for her, and while it would be upsetting to leave our home, it's a step we're willing to take."
Kate was diagnosed with cystic fibrosis when she was just days old, while her twin sister Megan is completely unaffected.
Kate suffers from a lot of abdominal problems and has a lung function of 90%, which is considered good for a CF sufferer.
However, Mr Gordon's concern is that the longer she goes without Kalydeco, the worse her condition will become.
The medic said: "I've no doubt the drug will become available in one form or another in the future. The future's bright for CF sufferers, but not for the ones who need the drug now.
"The fact that Kate has 90% lung capacity is seen as a victory now, but we don't know what it will be the next time she is checked. At best, it will stay the same, but it's likely to deteriorate.
"This time of year is particularly bad for CF patients, because what would be a normal virus can be fairly catastrophic, so it's all the more frustrating to be waiting on this decision."
The petitioners are calling for funding for the drug to be made available immediately, pending the SMC decision, and want health boards to introduce it if it is given the go-ahead.
It was hoped it would be considered by the petitions committee in December, but it will now take place in the New Year.
Kalydeco was licensed by the European Medicines Agency in July this year and has been approved by the US Food and Drug Administration.
However, the cost of the drug is high, with manufacturer Vertex pricing it at £182,635 a year, or £15,219 per person per month.
The SMC website shows that the drug is under consideration and a decision will be delivered on January 14.