What way is it too big Height? I shipped a mog to OZ in a high cube (extra height) container by removing wheels and unbolting stoneguards from brake discs and driving into container on discs in low range no damage was done . Have you looked at putting on flatrack ? HTSH
This may seem like very obvious but, try googling "australia to new zealand by RORO". I did this and there were lots of hits. Pick one and enquire.
I will be shipping a Mog with camper to Vladivostok from West coast US next year and that is how I started -with google
If you are doing it just because a carnet is good for only 1 year, be aware I had my carnet (with CAA) extended by a year using the services of a customs broker in Australia.
I'd drop an email to Maria at ATL Global. She has done a great job for us on Ro-Ro stuff, even pretty complex routing (Baltimore to Dubai, Dubai to Dar es Salaam), and she's very familiar with the layout and limits on various ships. Her email is maria@atlglobal.us and you can mention that I (Karl with the silver Landcruiser) referred you. She called me when I was not far from the Kenya / South Sudan / Uganda tripoint to give me a customs status update on one of our vehicles... at 6AM her time! Can't ask for better serivce than that.
I have shipped from NZ to Aust about 10 times, its not that hard if you have a good broker than can walk you through it. RoRo you will be paying approx 115 to 125 USD per cubic/m. Plus all the sundry fees charges etc etc etc. PM me if you want my brokers details.