Cats are prone to killing birds and wildlife and in Australia if you own a cat you have to keep it in doors during the night or you are fined if it is caught wandering
I doubt the cat is responsible for as much damage in Australia as people like to make out. The proof of this is Tasmania.
Only two subspecies of birds (the Tasmanian Emu and the King Island Emu) and one mammal (the Thylacine) have become extinct in Tasmania since the arrival of white man. None of these extinctions cannot be put down to the cat, yet Tasmania has plenty of cats - both domestic and feral. Many small mammals that have become extinct or rare on the Mainland are common in Tasmania.
The reason for extinctions on the Mainland are far more as a result of habitat destruction (which has been greater on the Mainland) and to the introduction of the dingo and the fox on the Mainland.
I once read a report that up to 80% of feral cats' diet is rabbit. They also take feral birds (such as blackbirds).
There were many cats on Macquarie Island but then some bright sparks decided to eradicate them to 'save' those nesting chicks that were taken by cats. Eventually all the cats were removed and the feral rabbit population exploded. This huge rabbit population ended up denuding the island of vegetation and as a result landslides occurred that killed the chicks in far greater number than the cats ever took.