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Their new son's capsule, Olson's wallet and other personal belongings were all inside the ute when it was stolen.
The couple had just purchased the ute about a week ago for their growing family, with new tyres added over the weekend.
However, the 27-year-old said a kind friend had immediately jumped in to lend them a car in the meantime.
And Olson, who works as a digger driver in Wellington, wanted to share a "massive thanks" to all those who had stepped in to help since the theft.
"Everyone has been so supportive ... with all the help we have been offered and all of that - it's been great."
Barnett's older sister Te Aroha Haami - who is just days away from welcoming a baby herself - has started a Givealittle page to raise money for a new car and to replace the essential items that were taken.
She explained on the page: "Having a premature baby is worrying enough but to now have to deal with a stolen car and contents at the same time is just adding stress to the situation."
As of this afternoon the couple's baby is yet to arrive.
Police have been approached for comment.