Hi
We have flown Air NZ a few times with our 2 youngsters in J and Y. The crew are so good with children and probably the best we have encountered - nothing was too much trouble. You are the best to decide which seating option is right for you. There is obviously alot of info about pro's/cons of car seats vs lap infants and bassinets and I think it can only be your decision as to what will work best for you and your child.
You are correct with the take off/landing/turbulence on your lap then the bassinet can be used at other times. They are not really 'secured' in it as such so a mobile child especially if awake in a bassinet needs very careful attention.
You can easily bf with the lap belt on- an extra pillow or 2 makes it a little more comfortable and easier!!
The Air New Zealand website has info about the car seat dimensions which may help see if your current seat fits or an alternative one would be needed.
Enjoy your trip.