Welcome to the HUBB!
People have transported their motorcycles to NZ for part of their RTW trip and if I was also going to ride around Australia for 6 months + id consider it, for your four month trip its right on the financial borderline, renting would be too expensive for this long, have you considered buying a bike in NZ ?
If you haven't already post a question in the Aus/NZ section re long term rentals/borrowing/buying a bike. Also under the 'Connect' tab above, look at the HUBB communities in NZ (9 of them) and maybe fire a message to them asking their advice, you may even find someone willing to loan/rent you a bike or at least point you in the right direction for buying.
Another angle might be to ask a motorcycle rental company if they have any bikes they are selling off or if you could get a 'Sale & Return' on a bike.
I just found this company on Google:
Also take a moment to put your location in your profile, so it is visible in the top right corner of your posts, this helps everyone know where you are from and what market you are (normally) buying/selling/riding in.