Original map: Wikimedia Commons - Author: Maximilian Dörrbecker (Chumwa) - modified slightly by me.
There are no Australian wild cats other then feral cats. In other words there is no species of wild cat in Australia. This is surprising as the Far East is a area of the world where there are lots of wild cat species. In nearby Indonesia there is leopard, Asiatic golden cat, bay cat, fishing cat, flat-headed cat, leopard cat, marbled cat and tiger. See wild cat by country.
Feral cats are not a wild cat species. Scientifically speaking they are classified as domestic cats: Felis silvestris catus.
This article is an attempt to explain why there are no wild cat species in Australia. There is nothing on the internet on this subject as far as I can tell.
The reason must be connected with the evolution of the world's land masses together with the evolution of the species of animal that we classify as the cat. These two long running events conspired to prevent the cat evolving in Australia.
The other possibility is that there were wild cat species in Australia but they were made extinct by human persecution of the cats or the prey upon which the cats fed. Technically this would be a possibility but there is no research to support it. It is a fanciful hypothesis.
Land mass development vs cats species development
Australia become an island 99 Ma ago, separating from a large land mass called "Gondwana". Eight to 20 Ma, in Europe, Asia and North America the first prehistoric cats developed Pseudaelurus.
It would seem that the isolation of the Australian continent prevented these prehistoric cats from extending their distribution into Australia.
A deep water channel called the "Wallace Line" separates the ecozones of Asia and and a group of Indonesian islands called "Wallacea".
This line divides the two areas in respect of species of organism. To the west of the line are Asiatic species and to the east are species of Asian and Australian origin.
During the last 2.5 million years there were "ice age glacial advances" causing the oceans to be 120 meters shallower. This would have resulted in the unification of Asia and Australia by way of the islands between the two but for the presence of the deep channel called the Wallace Line that has kept the continents apart for the past 50 million years in respect of their respective fauna and flora, long enough to prevent the evolution of the species of animal called the cat (Felidaefamily) on the Australian continent.
See associated page: Feral Cats of Australia