The a 45-year-old businessman and 37-year-old housewife have three young sons and are hoping to complete their family using the hi-tech genetic process, which is outlawed in Australia.
The woman had treatment yesterday, with surgery to insert two of her fertilised female eggs at the Los Angeles clinic of Dr Jeffrey Steinberg, who pioneered sex selection technology.
"I've got three boys and I wouldn't swap any of them for the world, but having a girl would be absolutely amazing," the woman said yesterday.
"I've got girlfriends with girls and they are really different to boys -- different attitude, different way of doing things.
"I'm not a prissy person and I'm not going to want to dress her up or anything, but I just want that experience of having a girl.
"Even our six-year-old once said, 'I think we should have a girl -- we've got enough boys'."
Her husband said he'd have been happy to have just their sons but wanted to give his wife the chance for her dream of a daughter come true, regardless of financial cost.