Do not start shipping the car until you have received the import approval.
I brought my 67 FB & a 260Z over from NZ using Conroy Removals; Akld to Brisbane; 1 x 40ft container with the 2 cars inside plus our personal effects (household goods) on a mezzanine shelf above the Datsun (the Muzzy had the front 1/2 to itself for safety, my preference); excellent service, was very happy indeed with their customer service. Car enthusiasts at both depots helped! So I'd use Conroy again.
However, be sure you understand all the costs involved plus the GST fee on car's value at this end. Do your sums, as in compare selling car in NZ & bringing money over with exchange rate vs what car will owe you or be worth in AUS $ registered on the road; for me it didn't make financial sense, but the fact that we'd need to ship other stuff over anyway plus the heart factor with long term ownership was the way I had to justify it. [My wife also talked me into bringing the recently restored Muzzy, I don't think she could stand the thought of me selling it then finding another one over here & spending yet more years in restoration work; so there's possibly a time factor to consider as well]. Don't forget to allow for compliance costs, I had to upgrade rear seatbelts from lap to lap/sash so extra anchor points were installed to approval. Not a big drama all up, but various costs are involved which all add up. And the NZ-AUS $ exchange rate is worse now that when I shipped.