Welcome from New Zealand!
I will not say you -need- 4WD to enjoy Overlanding. But, in the absence of it, you'll need to be extra-aware of your limitations, both vehicle and driver. The same obstacle a vehicle with 4WD would yawn at could be a serious situation for a 2WD vehicle.
A bit of good decision-making, along with a good tires, a shovel, and a set of recovery boards/tracks will get you to camp 99% of the time.
What you need will largely depend on you getting out there and seeing what you routinely encounter.