Hart is equally enamoured with her race-car driver beau, 36, revealing Kirkham – who is also a father to 6-year-old daughter Wren from a previous relationship – is an “unbelievable dad”.
“He is so hands on. They go on daddy-daughter adventures all the time,” the model shares exclusively with WHO.
“Everything’s an adventure with dad. The girls are so lucky to have him as a daddy. Baby is already a daddy’s girl. She lights up whenever she sees him, it’s really adorable!”
With Hart based in the US, she hasn’t been able to share her experience with her Aussie family and friends, but luckily she’s had her mum by her side during the first few weeks of motherhood.
“She was fortunate enough to get approved to come and be with me, which was amazing,” Hart tells WHO. “Everyone else has been FaceTime – thank god for that!”
Her sister and fellow model Ashley, 32, has also been on hand for plenty of newborn cuddles.
“Ashley is the best aunty already,” she adds. “We see her a few times a week.”
When deciding on a name for her newborn, Hart recalls always loving the name Baby after hearing it in the 1987 film Dirty Dancing as Jennifer Grey’s lead character.
“I first heard it in the movie Dirty Dancing and always thought I’d love to name my daughter Baby,” the blonde beauty told WHO’s sister publication People magazine recently.
“I was hesitant to ask James about it at first but we just weren’t landing on a name. Finally, probably a month before she was born, I said what about Baby, and he said, ‘Oh my gosh, I love it.’ It’s felt right ever since.”
Hart adds that she also wanted to carry on a family name from her side when naming her daughter.
“My legal name is Jessica-Rae after my mother Rae and I wanted Baby to have something relating to me in her name as, naturally, she takes Kirkham as a last name,” the model continued. “So we’ve given Baby the hyphenated Rae, too. Her legal name is Baby-Rae Kirkham, but we just call her Baby.”
The model confesses she’s been in a “little newborn bubble” with Baby-Rae and her fiancé – who proposed to Hart at her baby shower back in October, just weeks before their little one’s arrival.
“I don’t know what’s going on with the world at the moment,” she shared with People. “It’s just me and her getting through each day. We’re both learning together. It’s really cool.”
As for when she’ll return to Oz to introduce Baby to her loved ones, Hart admits she “cannot wait” to make the trip when it’s safe to do so.
“I haven’t wanted to be back home more than I do now,” Hart tells WHO.
And it seems when they do head Down Under, Hart and Kirkham might have some house-hunting to do!
“My dream is to live between LA and Australia,” she adds. “James and I are working towards that!”
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