"The first child of NZ has been officially coronated," one person wrote.
Another added: "What do they say? That Dad has a great sidestep."
"That's just what a blue/green coalition will do to the young as well," another joked.
One person commented that the "Bird of the year has bestowed its greatest honour."
This is not the first time Gayford has shared Tweets on New Zealand's "First Baby."
In February, the father shared a photo of a present Neve received from a Orewa retirement village resident.
"This arrived with a nice note from a workshop in a retirement village in Orewa. Thanks Murray!!," Gayford wrote.
"We are not far off putting it to good use as the little rug wriggler's co-ordination is fast catching up to her travelling ambitions."
He also shared previous presents Neve received from world leaders, including a bizarre hat from the Prime Minister of St Lucia.