"We saw lots of police cars on the way, and if one of the officers had stopped us, I would have had to deliver our son on the roadside," Ms Thompson said.
"It was a very quick labour in the end.
"We got to the hospital about 6am, my waters broke at 6.05am, and my son was born nine minutes later," she said.
Ms Thompson said her new baby looked like his father, who was absolutely chuffed, and her other son two-year-old Waipihangarangi was starting to bond with baby.
He wanted to kiss and cuddle his brother all the time, she said
"I have described our new baby on my facebook as hairy, healthy and handsome. He has full head of hair just like his older brother. He's beautiful," she said.
"We haven't been able to find a name for him which feels right yet. But we weren't able to find the right name for my oldest son for nine months, two weeks, so it's not surprising," she said.
Ms Thompson said when her and her partner did choose, they were likely follow the family tradition of choosing an ancestral name.
During her pregnancy Ms Thompson repeatedly told her family she didn't want a New Year's Day baby.
"My partner and I were very surprised but in the end it doesn't really matter, he's a lovely baby. New Year's Day will a definitely be an extra special occasion in our family from now on."