I went 2 year ago, but only the north island , from what i saw travling round there werent great numbers of rabbits, but its hard to guess when your mainly on the road.
i have herd that the south island has big populations of rabbit.
theres lots of land and forest owned by the government, and from what i was told you DONT need permision here. but obviously do on farm land.
if ya like fishing , you only need a licence and can fish any where , non of this day ticket carry on. also herd gun licence is easy to get hold of. and theres no closed season on the 8 species of deer thay ha