Nz orginally had birds, bats but no other ground mammals. Everything has been introduced so its fair game, especially the brush tailed possum which does more damage to NZ native forest every minute that every one of you if I let you loose with hotsaws. (they eat 20,000 tonnes of vegitation every night nz wide) Possums also do huge damage to the native bird population by taking eggs and chicks and competeting with ground birds for nests.
If you find one in the tree its fair game, your doing the enviroment and your profession a great favour, if you can get the furry maggot.
NZ is pretty good for hunting, any time of year you can hunt deer, pigs, goats, wallabes and of course possums.