Adam:
There are no arrawana in Australia, I believe they are native to South America. We do have two endemic osteoglossids, though, common name 'saratoga' (genus Scleropages). They shouldn't really qualify as sport-fish, having the fighting characteristics of a pelagic eel, but both species will take a fly with gusto and will leap occasionally so they are often targeted by fly-fishos.

Here's an average one caught last October:

...and here's the biggest one you're ever likely to see, caught many years ago in the gulf:

The best recipe for saratoga is:
Place one saratoga and one old sandshoe in a kerosene tin full of water, boil for 3 hours, throw away saratoga and eat the sandshoe.