Last time I did it was 2016 for a competition. Needed B709 from Oz AFP, declared all imported and exported ammunition, and of course NZ export/import permits. Also required an account with Oz customs to get a customer reference number for the B709 and Restricted Goods Export permit. Flew Air NZ via NSW, then drove to ACT. Most of our dealings was via SSAA so you're probably best to hook up via them.
http://www.ssaa.org.au
Overall I'd rate it a 3/10 for hassle, best thing we did was make 3 photocopies of everything including our passports to hand over to customs on arrival in Sydney, showed we were prepared and weren't fucking around. By comparison, the 2018 trip to the USA went even smoother once ATF was sorted.
disclaimer - I went for competition so had invite letters from the organisers which I suspect helped the paperwork. Your mileage may vary.
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