Month-long Summer NZ travel with 3-year-old: what do you think? Should we rent a camper van for part of our stay? Do you have other suggestions for taking a 3.5 yr old in tow?

Yes, the maximum time I would campervan for would be 2 weeks. You may go a bit cabin crazy for longer periods. But people do spent months in the bigger motorhomes. If you pay the big money you get all the comforts of home.
Motorhome travel stuff
http://www.newzealandatoz.com/index.php?pageid=13

I'd settle for a motorhome. You won't need to be packing and unpacking everyday plus you can prepare your own meals, and settle your child into a routine of sorts. Plus if you are staying in caravan parks/camping grounds, there will be other children to play with, playgrounds and swimming pools, camp kitchens, laundries etc, to make life easier.

Thanks for the replies so far. keep 'em comin'!

We did six weeks in a campervan (3wks in Oz and 3wks in NZ) with our 3.5 year old. Toyota 3/2 berth and togetherness wasn't a problem.

But you do still have to pack up/reconfigure the van to leave. The nice holiday parks also have cabins (although they seem to sell out before the camper spots and might need reservations). You might consider just renting a car and staying in the cabins. The price can work out similar.

Also, you can prepare your own meals in the holiday parks whether you are staying in the cabins or in a van.

As far as traveling with a 3 y.o., bring a portable dvd player so you can have a break!