Native Australian carnivorous animals are mostly the dasyurids, or carnivorous marsupials. These include: Tasmanian devilquollphascogaleantechinusdibblerkowariplanigale. The extinct Thylacine, or Tasmanian tiger, was a carnivorous marsupial. The dingo is considered to be a native carnivore, although it was originally introduced to the continent by the Aborigines many thousands of years ago.
Non-native carnivores include dogs, cats and foxes.
Introduced non-carnivores include bunnies, I believe, they were a bit of a disaster, if memory serves. And the predators introduced to clean up the bunny problem just caused more problems.