Lucky and Emma Price are just like any new parents — happy, proud and tired.

Their baby son Bertie is cradled in his father's arms.

But the story of how this couple met and came to start a family is anything but ordinary.

New father Lucky started life as Eliza, the youngest of four girls.

'Something felt not quite right'

Eliza felt no connection with the girl in the mirror. ( Supplied: Lucky Price )

"I never felt quite in my own skin, something felt not quite right and the way that proliferated in me was anxiety," Lucky told 7.30.

"To feel a complete disconnect with who you look at in the mirror felt awful and frightening."

In her early 30s, Eliza made a decision.

"After seeking the right medical help and talking to a lot of people and going through counselling and with the great support of my family, I decided to transition my gender from female to male or to be more male identifying," he said.

Eliza became Lucky.

"I started off on New Year's Day in 2014," he said.

"I started on testosterone treatment and sometime after, maybe about 18 months ago, I had top surgery as well, so I removed both of my breasts.

"I am much happier, absolutely, without a doubt, which is part of the reason I chose the name that I did.

"For Eliza to become Lucky, that is exactly how I feel about this experience."

And there was more happiness to come.

Lucky in love

Emma and Lucky ( Supplied: Harold David )

Several months after he began transitioning, Lucky met Emma in her bar in inner Sydney.

"I was behind the bar, I went around the bar and said to my colleague, excuse me I just need to give this human a hug," Emma recalled.

"So I went around the bar and connected with Lucky and the rest is history."

Emma now has a tattoo on her forearm declaring "Lucky in Love".

The couple decided that the next step was starting a family. They consulted Monash IVF.

"We chose to look at anonymous donors as opposed to other avenues that people in our community might choose to take," Lucky explained.

According to Dr Bronwyn Devine from Monash IVF, there's been a steady increase in the number of gender diverse couples seeking fertility treatment.

"Definitely we're seeing more trans people coming through, looking to either preserve fertility, or start a family or add to a family," she told 7.30.

"Just because people have gender identity that differs from their biological characteristics it doesn't mean they won't be fantastic parents.

"And the technology is there. It's my job as a fertility specialist to help people have a family when there are challenges.

"Why not help all people have a family?"

For Lucky and Emma, the most difficult part of the process was the wait for a sperm donor, which took a year.

After that things moved very quickly.

"It took first go. Unbelievable. And stayed on board too, which is statistically very low. So we're very lucky," Emma said.

Dr Devine agreed Emma had been lucky.

"Here's a woman who probably hasn't had fertility challenges in her life, other than the fact that her partner doesn't produce sperm, but she was very lucky at 42 to conceive first time," she said.

'He's an awesome guy and he's our son'

Emma Price and Lucky during Lucky's transition ( Supplied: Harold David )

The couple also decided to marry. That was possible because Lucky had begun transitioning to male.

Under Australian law after sex affirmation surgery a person can legally change their sex.

"Once I had my top surgery I was able to change the gender marker on my birth certificate which made me legally a male, which meant that we were then able to legally marry," Lucky explained.

For now, Lucky has no plans for any further surgery.

"I am perfectly happy with my downstairs business the way that it is. That is a path for other people, but not something I connect with at this stage," he said.

The couple's son Bertie arrived a week before his due date and was born by caesarean section.

Mother and baby are well, and Lucky is thrilled.

"He's an awesome guy and he's our son," he said.

Emma Price cradles newborn Bertie ( Supplied: Emma Price )

One day Emma and Lucky plan to explain to Bertie the whole story about how he came to be.

"We're always going to be very honest with him about how much we wanted him and what we had to do to make him come and be part of our lives," Emma said.

"We will get to know each other over the years to come and he'll know all about daddy and how I came to be," Lucky added.

And what do they wish for Bertie's future?

"I wish for Bertie to be his absolute true self and I will support him and love him whatever that is," Lucky said.

Lucky and Emma say that in the end, they're just a couple who fell in love, and have been lucky enough to start a family.

"It's the most extraordinary, ordinary thing," Emma said.