While having a giant nature reserve in New Zealand sounds great, I think that unfortunately it would be too tempting of a target to avoid. Europeans would know about this "terra nullis" from at least the 1650's onward, after Abel Tasman's voyage. While the Dutch East India Company might send follow-up expeditions to the island, the lack of trade probably ends any attempt they make to settle it-they weren't really about settler colonies, South Africa notwithstanding.
The next wave of colonization would come in the 18th century. We could see French settlement of the island, with this world's version of Bougainville leading an expedition with Acadian refugees from the New World to New Zealand instead of the Falklands. If France diverts some of the colonists that they sent to die in Guiana IOTL to *Bougainville, the French New Zealand colony could very well take root and survive. Otherwise, the English take it as per OTL.
I will say, while the two main islands will be colonized by humans, its possible that some of the larger 'offshore' islands of the New Zealand archipelago could have European settlement prevented for any number of whacky schemes. Maybe its set up as a preserve for New Zealand fauna, and moa are released on the island and are able to survive; perhaps more distant fauna are released on the island due to some aristocrat's whims, and we end up in a situation where the Tasmanian tiger or some Asian animals have a breeding population established on the island.
At the time, European racism often treated Indigenous people as animals, as has been pointed out already in this thread. However, occasional humanitarian concerns could break through, and we could very well see a population of Aboriginal Australians or Pacific Islanders settled on New Zealand land to 'save' them from both paganism and the threat of a rival European power.