The television and radio presenter managed to film another season of Fish of the Day over summer but said some days he realises he's wearing a "ratty old pair of track pants because that's all you pulled on at 5am and you haven't shaved, and you're going 'Oh boy'".
Gayford said he is often approached by other dads in the street when he's pushing Neve in a buggy.
"They get so excited and start chatting about the good aspects and the tough aspects and I think that's quite nice to hear and to talk to as well."
Neve wasn't part of a playgroup yet Gayford said, mainly because he and Ardern had to split their week between Wellington where the Prime Minister is needed, and Auckland where the family lives.
He did have plans to take her to baby swimming lessons but by the end of the week the family just wanted to relax.
"Before you know it's Friday and you just want to catch your breath before it's Monday again."
And while Anika Moa's baby tunes had been a firm favourite to play to Neve by Ardern, Gayford preferred his own music tastes and said he planned to convert Neve.
"I'm trying to bring her up with a more advanced palette and bring her up on a little bit more of 'my' music."
It's not the first time Gayford has opened up on fatherhood.
He regularly tweets about incidents and events involving Neve including one where he implied the littlie vomited all down his clothes and another where he posted a picture of a child barrier drilled to an open doorway with the caption: "You Shall Not Pass."
Gayford's down-to-earth humour about being a dad has resonated with parents around the country.
On April 6, after daylight saving ended, his tweet "Hmm, seems that no one has put Neve's clock back for daylight saving" attracted 43 comments and 1600 likes.
Gayford was talking to Tame to promote the upcoming Planet Earth 2 Live in Concert Show alongside the Auckland Philharmonia Orchestra , which he will narrate.