Status varies from state-to-state and different for different land tenure. In Australia whatever (unbranded non-native) animals on 'your' land are your responsibility and your own to do what you like with. You can make money from them but if their numbers become too high the govt may step in and force you to reduce their numbers. In the extreme the govt will come and do this and send you the bill.

A great deal of the camels are on aboriginal owned land. That is a special kind of tenure - mostly not freehold but not public or crown lease either. The owners can make money from the land just like freehold and leasehold but the crown can also step-in and do certain things, like control feral animals. There is some conjecture with regard this law as it is covered by both state and fed laws (somewhat conflicting too) and this is still the subject of ongoing legal action.

Kamilaroi - the problem with us and the Central Desert people has more to do with cultural issues. They do not want to see camels laying dead on their land but they are OK for someone to catch them and slaughter them elsewhere. Somehow however the govt departments seem to convince them that it is OK to shoot them from helicopters.... no doubt the hold things over them when they object. "Let us shoot them or you dont get your new houses" type stuff.

You may be right too about getting to know people better.