We're flying from Australia to New Zealand and have a few hundreds of AUD left. Is it possible to exchange them to NZ dollars in New Zealand or we need to this from Australia?
Very, very easy. Any bank in NZ will happily exchange those for you, or indeed as you step off the plane, there are several currency exchange places at all the international airports.
Be aware that the airports can sometimes offer worse rates than banks in town - but it depends how much you're exchanging of course, as to whether bothering with the effort is worthwhile.
The large Australian banks all have branches in New Zealand. In particular, the ANZ (Australia-New Zealand) Bank was set up to serve both Australia and New Zealand.
Not a problem at all. If you arrive in Auckland or Wellington you can exchange your money in the Airport or anywhere in downtown, or near tourist traps anywhere else in the country. Some ATMs in central Auckland can even dispense AUD if you plan to go back there later...