Ms Hart, an advertising professional, previously had two sons from a husband in London and a partner in Australia, but both babies died. She learnt that she was the carrier of a rare genetic disorder that affected sons but not daughters.
At the age of 42, she decided to try one last time for a healthy baby using IVF. And soon after Leila turned one, Ms Hart decided to try to track down the father.
Ms Hart's own father was a West Indian film extra who met her Australian mother in London shortly after he returned from playing Omar Sharif's bodyguard in the film Lawrence of Arabia.
The couple separated when Ms Hart was young. She later tried to find her father in England, but learnt that he had died shortly before her arrival.
Determined to find her own daughter's father, Ms Hart discovered his identity through a series of internet searches based on his name "Scott" as well as his profession as a cattle breeder and his role as a football coach.
Rather than contact him directly, she did so through the official IVF register. He was not legally required to meet Leila until she turned 18 but agreed, especially after he received a photograph of his baby and saw how much she looked like both him and his four other children from two previous marriages.
"It was surreal," he said. "I was looking at this little girl - she looks like my other kids and like me.
"Blond hair, blue eyes. It was overwhelming at the start. It wasn't really my daughter, but it was. At first, I didn't know Aminah so I didn't show much emotion."
Ms Hart said: "We were very tentative, but the rapport was really easy. The first thing for me was, phew, he's a nice guy."
They agreed that Mr Andersen would become a part of Leila's life and they all began to meet once a month and then once a week, even though she lived in Melbourne and he lived 80 miles away, on Phillip Island, off the coast of the state of Victoria. "My children all adored her," he said. "Leila is just a happy kid. She didn't want to go home and she cuddled the boys the whole time."
The couple both separated from their partners and a mutual attraction developed, although Mr Andersen was apprehensive because "I thought she was totally out of my league".
Eventually, trapped on the island because of a road closure, they went for a beer and she told him: "I think you should kiss me."
"So, romance was born," Ms Hart told Australian Story, a television documentary series. "I just essentially say to people the cart well and truly came before the horse and the horse caught up eventually and hooked itself on.
The couple became engaged during a holiday in Thailand, after Mr Andersen went to buy milk for Leila in a village and returned with a ring. Their extraordinary marriage has attracted attention from screenwriters, including from Working Title - the creators of Love Actually and Bridget Jones's Diary.
"I presumed that when I was elderly someone might knock on my door and say: I am your 30 year-old-son or daughter,"' said Mr Andersen.
"This just seems amazing."
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