Are Compound Bows Legal in Australia?

This is not legal advice.

Please check your own state or territory for current weapons laws.

Currently and to the best to our knowledge there is no law in any state or territory to prohibit buying, posting, owning or using a compound bow or recurve/ longbow in Australia. This means that there is not even an age limit for the purchaser (although you must be over 18 to purchase items on some online portals such as eBay). That being said, there are still laws governing the transportation of weapons and the carrying of weapons in most states. For example, any adult can buy and own a knife but there are still limitations on carrying a knife in a public place like the shopping mall or on the train or even in your own private car. If a knife was used criminally then there would be charges relating to the use of the knife even though possession of the knife is legal eg. armed robbery. 

In the same say if you were using your archery set in your own back or even front yard and a neighbors property or person was damaged then this would obviously still be an offense even though the use of the equipment may not be prohibited. In the same way that using a tennis racket to damage or injure property or persons is still an offense and in its use could still constitute a deadly weapon. 

No license is required (as far as we are aware) to use your archery set to hunt animals, for example. There are laws, of course, about what animals can be hunted and where they can be hunted and the humane treatment of even feral animals, but no laws at this stage relate to limitations to using some kind of archery set be it a compound bow or longbow/ recurve bow for the use of hunting. This means that you are allowed to hunt (usually just feral) animals on private property given permission by the land owner and even on government land and reserves so long as you arrange the correct documentation and permits.