JAL accepts rabbits as checked baggage. I think they will be your best bet. Caveat: They mandate special rodent transport crates for rabbits. Those aren't readily available in pet stores.

Edit:
JAL will only restart the route in March (at least that's the plan, anyway). If you have to fly earlier, you 'll have to send the rabbit as cargo using one of the few airlines currently flying. Try Etihad (MEL cargo office: +61 448 268621) , and Qatar ([email protected]).

There are no airlines currently flying the route allowing pets in the cabin, and JAL ist the only airline scheduled to fly this route one-stop accepting your rabbit as checked baggage (reasonably priced!) . If you want to take it in the cabin you'll need to wait until the European airlines (LH) restart the route with their own flights which will take months if possible at all this year.