You could tee-up a hunt with local bowhunters in the areas you visit. Look me up if you come through Katherine.
An even better bet would be to firstly research the species you really want to hunt, and if you find that you're really keen to nail pigs, goats, donkeys, horses, or camels, it's pretty-much a sure thing to get work on a station in an area that has some of that game, and then you're in like Flynn. Stations are desparate to employ people, because the pay's not great and many of the able-bodied fellows are going to the mines. You'd be able to glean quite a bit of experience and knowledge just working on these places which would benefit you when you went hunting there on your weekend or in the evenings (although there are some times when you'd be flat-out from dawn 'til dusk working).
If you want to hunt pigs, donkeys, and horses, then try the cattle stations in the Kimberly, Top End, or Gulf and Cape (though without the donkeys in these last two). If you want to hunt donkeys, horses, and camels, then try the stations around the Alice or around Newman. If you want to hunt goats, then try the sheep stations around Carnarvon. They're all desparate for workers.
I hope this helps.
Ben