Cameron Pinceus is the head chef at a restaurant in Hobart's Salamanca Place — but he never thought the first slice of liver he'd give his daughter would be his own.

And now feisty little Mila is more her father's daughter than anyone might guess.

You'd never know, as she rockets about in her walker, that the one-year-old is recovering from lifesaving surgery.

Just weeks ago her entire liver was replaced with a fifth of her father's.

The rare living-donor liver transplant is believed to be the first father-child organ donation in Victoria.

Cameron is recovering almost as well, but is still sore.

Mila became seriously ill while visiting family interstate with her parents. ( ABC News: Patrick Rocca )

"His new nickname is Spare Parts," said Mila's mother, Nicky Browning.

But it was no laughing matter just over a month ago when Mila's health started to go downhill after visiting family interstate.

She failed to respond to treatment back home in Hobart and was near death when her liver suddenly failed.

She was transferred to Melbourne and into the care of surgeon Graham Starkey, of the Liver Transplant Unit at Austin Health.

"It's difficult to predict exactly how long Mila had, but we were very concerned that she had days to live," he said.

Mila was put on the priority waiting list for a new liver. ( Supplied: Nicky Browning )

Doctors still don't know why her liver failed. Their best guess is that it was an uncommon reaction to a common virus.

Plan B becomes Plan A

As her condition deteriorated, doctors made Mila an urgent priority on the waiting list for livers from deceased donors.

Meanwhile, both parents were screened for compatibility as living donors.

Nicky wasn't a match — something that still makes her emotional — while, luckily, Cameron was.

Mila remained in high spirits in hospital. ( Supplied: Nicky Browning )

Mr Starkey says that strike rate is actually very typical — in his experience as a surgeon, only half of parents would even be eligible for such acts of anatomical altruism.

"It's by no means a given that the living related transplant is an option at all. For a lot of people, it's a non-starter," he said.

Living-donor liver transplants are nowhere near as common as those that happen with kidneys.

It's not the preferred option because of the inherent risks of the operation and stress on the family.

In Australia, the procedure is only performed on children in emergency situations.

In fact, until Mila's surgery, there had been no living-donor liver transplants in Australia since 2017.

But when no other donors emerged for Mila, Nicky said "plan B became plan A".

'A really tough day'

For Cameron, there were no qualms.

"When they said that I was a match, I thought, at least I can do something now. You always want to do something for your own child … I didn't hesitate," he said.

But the stress for Nicky of having her husband and child both under the knife, in separate hospitals, is still visible.

Cameron and Mila are recovering well and will soon return to Hobart. ( ABC News: Patrick Rocca )

She becomes tearful as she describes the scary time.

"It's like every single member of my immediate family was having surgery that day," she said.

"So it was a really tough day."

Fortunately for the recipient, the procedure and prognosis are much the same, whether it's a liver from a living or deceased donor.

Mr Starkey said the small portion of the liver that's generally taken for children — in this case, from Cameron — fit seamlessly in Mila's body.

"The left lateral part of Cameron's liver was a perfect match for Mila," he said.

"It fitted in nicely and worked straight away.

"So she came off the operating table with a functioning liver, having gone in with one that was just barely clinging on."

Mila's new liver will grow with her as she gets older. ( ABC News: Patrick Rocca )

Being the only human organ that grows back, Cameron's liver appears to have already regrown to the size he needs, just a few weeks after surgery.

Mila's adopted liver will simply grow with her.

"The liver is an amazing organ like that. It's got a great capacity for regeneration and full growth," Mr Starkey said.

"And we hope and expect that it will serve her well for many decades to come."

Austin Hospital surgeon Graham Starkey said donating an organ was the ultimate act of generosity. ( ABC News: Patrick Rocca )

The ultimate act of generosity

Mila's story, though heart-warming, is another reminder of the precarious situation facing anyone suddenly dependent on donated organs.

Mr Starkey would prefer that no parent had to go through Cameron and Nicky's experience.

"Australians, we like to think of ourselves as a generous community, and this is the ultimate act of generosity," he said.

"I think Australia should aim to have an organ donation rate as good as anywhere in the world. At the moment we are not quite up there with part of western Europe, so we can do better."

Mila will soon return to Hobart with her parents.

They tried for two years before conceiving her so they now call her their "twice-miracle" baby.

To register for organ donation, go to donatelife.gov.au.