DO NOT joke with Ag. and Fish.! They have NO sense of humour, any more than Customs do.
You will fill out a form on the 'plane, which asks if you have been on a farm and various other places away from the city. Do NOT tell lies on it, they are good at detecting them. We even have a TV show about it.

Do not bring food into NZ, unless it is processed and packed.

Do not bring anything but prescription drugs in, and bring the prescription. You and your seat surroundings will be sniffed by the drugs dogs, and if they find anything, out you go again!

It sounds draconian when written down, but it's much more relaxed once you are in.
Oz is just as particular as NZ.
There are ex-hire motor caravans for sale here.