There’s a few - but restricted to bats and rodents. They’ve been here 10-15 million years. They are generally termed native and lumped with marsupials.
After that you get the Dingo [native dog], arriving as a commensal of Aboriginal people maybe 5000 years ago, although there are some claims for earlier dates.
All the other placentals you’d encounter in the wild in various parts of Australia - Old World rats and mice, cats, dogs, fox, goats, rabbits, pigs, buffalo, horses, deer, camels, children - are derived from imported animals brought by Europeans after 1788, and are generally distinguished as ferals. They have not lived in Australia long enough to have evolved into deadly and voracious man-eaters, and so are not considered worthy of being native.