Couple honest questions here--What d'you do with the cat once its been shot? Also--why shoot it? Would it not be better to leave it, and let it gobble bunnies?
That's true to a degree but it depends on the type of landscape the cats are removed from.
Macquarie Island is an example of where eradicating the cat population resulted in an explosion in numbers of rabbits, and feral cats shot on farm land generally have a diet that is 80% rabbit, the remainder of the diet being made up of birds, mice, frogs, reptiles etc..
That changes once you move into the mainland forests. Rabbits don't breed well in our native forests as conditons don't suit them, so the cats and foxes that live in those areas depend on native fauna for the bulk of their diet. Cat's also climb trees which means smaller tree dwelling marsupials like the phoscagal and ring tailed possum are easy prey. One type of sign I look for when tracking cats in the forest are trees with a small collection of possum tails laying at the base.
One thing to note is the deeper into the native forest you go, the poorer the condition of the foxes, but not so the cats. This is a good indication of the cats success as a predator
The other problem with feral cats is if rabies were to find it's way into Australia it's been proposed that the feral cats and foxes would be the most likely vectors for transmission of the disease.
These are some reasons why a good feral cat is a dead feral cat... as well as what marlin VS said