There was no local experience to share knowledge from, and limited medication in the event of the body rejecting the transplant.
That operation was luckily a success, and now, the hospital is celebrating its 25th anniversary, with 116 transplants to its name.
It comes at a time when Australia is still behind in its organ donation rates.
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Scarlett McGowan was just a few months old when she was diagnosed with dilated cardiomyopathy - a rare condition in which the heart becomes weakened and enlarged and cannot pump blood efficiently.
She was placed on the waiting list for an urgent heart transplant.
The suitable donor was eventually found.
Her mother, Sam, says it was a bitter sweet feeling knowing her daughter would be receiving the heart of someone else's child.
"That whole day I thought about that family because their child would have been wheeled to theatre and not come back. And there's guilt and there's sadness, and there is, every anniversary of the surgery we stop and think about them and special occasions I still stop and think about them when we're pleased that we're seeing her birthday and her Christmas, I think about them on their Christmas's. Sadly, their circumstances wouldn't have been any different, so what they did was a very selfless act at such a desperate time for them, so we're incredibly grateful."
Scarlett is now a healthy, lively four-year-old and is one of several patients who have received a transplant.
The head of the Royal Children's Hospital heart transplant service, Doctor Robert Weintraub, says it's a process which requires ongoing treatment.
"The operation itself is not all that complicated, it's the treatment, it's the way of life, it's need to take regular medication, to have fairly regular follow-up and medical attendances - that's what really constitutes life after a transplant."
Patients who require heart transplants go on a waiting list, and there's often a small window of opportunity to perform the operation.
It's when hours and even minutes become critical.
20-year-old Rebecca Peters - who had a transplant when she was seven - remembers the day her mother received the call from the hospital.
"I was at school, and my mum came running into the classroom, crying and screaming, "come on Rebecca, we're going to the hospital, you're going to get a new heart" and I was like "I don't want to go, I'm in art class" and I just remember my parents, that whole emotional journey for them must have been. I can't even imagine what they went through but to this day, I've lived life. I've been so lucky."
And yet so many other patients aren't.
In Australia, more than 100 people are waiting for heart transplants at any one time, often up to two years.
There are simply not enough donor hearts for the number of people who need a transplant.
18 year old Tyler Airey, who had a heart transplant last year, says there's a lack of community awareness of the shortage.
"I don't think anyone would have a problem donating their organs, I think it's just a matter of people don't get around to filling out the forms and making that step."
Rebecca Peters agrees, and says discussions around organ donation should be integrated into school curriculum.
"You can start small, and start embedding the idea of a special gift and really tailoiring it to children, so when they do get to the age of 18, they actually have a fairly good idea of what organ donation is. And they don't know that if one person passes away, they can improve or save up to the lives of 7-8 people."
Australia is currently ranked 17th in the world in terms of its organ donation registry.
There are calls for "presumed consent" laws to be passed, such as in Spain, Belgium, France, Norway and Italy, where everyone is considered a donor unless they specify otherwise.
The average life span of someone who has a transplant is 10 to 20 years following the procedure.
Sam McGowan, whose daughter Scarlett underwent a heart transplant, says the operation was a difficult time for her and her family and there's no reason why everyone shouldn't be a donor.
"I think there's some kind of, something in a mother's brain, parent's brain, that doesn't let you think the worst. I think I did. But I never let myself go down that path. But I appreciate how close we came now, particularly when you think about the donor and that family. You know, we were a hair's breath from being in the same circumstances. We walked away with our child, they didn't. It's a very selfless gift."
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