Be careful doing this. ETAs can only be applied for if you're out of the country. So you would have to fly to New Zealand and apply for it there before coming back into the country. Make sure you follow the instructions carefully as there's a 3 year exclusion period if you violate the visa terms.
You might want to look at applying for a tourist visa. These can be up to 12 months long and as long as you have the cash to support yourself, the authorities are pretty good about it.
[broken link removed]