And yes except for hog deer there's no tags for ferals ( a game licence is $ 25 bucks a year). And starting from the big to the smal you have camel ,buffalo, ban tang castle, scrub Bulls , wild horses, donkeys, sambar deer,Russia deer, chital deer( axis I beleave to you) fallow deer hog deer, red deer, foxes rabbits feral cats pigs goats ... But the only native you can hunt in most places is dingos
So again I'd get in touch with that Alice springs bow hunting group as there's a hell of a lot of camels between Alice and Uluru ..someone might help u out
I'd say you will be gob smacked by the countryside it's a stunning though bleak old place ..
Ps if you have Osiris email pop him a note , he might have some ideas
Enjoy