Cats are an introduced species in Australia
Cats are excellent hunters and may help to reduce the rodent population if they are allowed outside, but cats will also hunt other animals. Given the opportunity, a pet cat will also try to catch birds, lizards and small mammals, putting our wildlife at risk. And we shouldn't blame the cat, it's in its nature to hunt.
Of course, it is not acceptable that our pet cats injure or kill beautiful fairy-wrens or cute honey possums. The only way to prevent the death of millions and millions of Australian wildlife is to make sure that pet cats stay at home.
Over 40% of Australian pet cats are now being kept indoors. If you are the owner of a feline companion, you may want to consider joining the number of cat owners who contain their pets. You can help protect our local wildlife, and, what is perhaps even more important to you, provide your cat with a safer environment where it is not put at risk of being hit by cars, of being injured by dogs or other cats and of catching and transmitting serious diseases such as toxoplasmosis. Check out the Safe Cat, Safe Wildlife initiative.
Roaming domestic cats are capable of travelling considerable distances and may venture into nature reserves. This puts threatened species at risk. Critically-endangered Ring-tailed Possums for example, are one of the many species that have been attacked and killed by roaming cats.
Fact sheet about the impact of pet cats on wildlife.
Further reading:
https://invasives.org.au/our-work/feral-animals/cats-in-australia/pet-cats/
https://cdn.environment.sa.gov.au/landscape/docs/hf/cats-wildlife-gen.pdf