Is there anything else important to know when flying around in New Zealand when compared to Australia?
Yep, the weather and the topography.
The weather can change rapidly and be quite different over the space of a short distance.
The topography means poor VHF coverage in many areas and the need to fly through valleys to get places. Flying in situations where there is no natural horizon.
A lot of you Aussies fly straight lines which is fine in OZ but doesn't work over here where due to weather and topography means having to fly around weather and terrain.
Ontrack is correct re Milford. I would recommend a trip to Milford BUT only if you go with or take a local instructor from somewhere like Queenstown or Wanaka.