In just 12 hours the tweet has received over 5800 likes and 840 retweets, with people praising the stay at home dad for his support.
One Twitter user wrote: "I can't imagine how hard it's been in your household this week, but you must be incredibly proud."
And another tweeted: "Her mum is just amazing. Showing the world how to lead a country and earning so much respect in the process."
And it looks like when Neve's ready to take her first steps, she'll have a delightful little red trolley to steady her, sent from "Murray" at a retirement village in Orewa.
Earlier this month, Gayford shared another of his adventures with Baby Neve: A particularly messy moment in which a Kereru had pooed on her.
He later tweeted that Neve had the last laugh when she vomited down her father's front, on his All Birds and over a rug in Premier House.