Isn't New Zeeland part of the continent that is Australia?
Personally I think that continents are a convenient yet silly way of dividing the world, and New Zealand is a good example of that. The usual definition of the Australian continent includes only the country of Australia as an island-continent. But if you want to include New Zealand and the other Pacific Islands, saying Oceania or even Australasia as the continent name is better. If you ever told a New Zealander that New Zealand was part of Australia, well, you would be looking for your teeth on the ground very shortly thereafter