Most likely a pre-European introduction of horses to Australia would see the Aboriginals hunt the horses to extinction, similar to what happened in North America. But, in the case it doesn't, Australia could be very fertile land for a steppe nomad type civilisation. I actually mentioned it in a college paper on the Plains Indians, once.
The main issue is is that with horses you are limited to certain regions of the continent compared to with camels, which can range anywhere. The quality of Indonesian horses might be an issue, although going by the Comanche example, any Australian horse civilisation will rapidly learn how to breed better horses.
That seems likely to me. Even with the horse they'll still be lacking good agricultural crops.
They don't need crops, the Plains Indians were either not farmers or had abandoned farming. At worst, they might need someone to supplement their calories with once they put too much pressure on the kangaroo and emu (as with the Plains Indians)--the Murray River area had many semi-agricultural groups with intensive (but not
agricultural) yam harvesting. If the horse nomads are putting such a huge demand on the yam farmers, maybe that might stimulate a domestication of the pencil yam, murnong, or other suitable crop? I believe there is also a species of yam that is found in New Guinea which is farmed for food but never was in Queensland where it is also found--but the rainforest or the Great Dividing Range in general is bad horse nomad areas, so it would have to be the pencil yam. Western Australia also has some interesting plants too, but getting a horse civilisation there is harder than getting one to New South Wales/Victoria because of the terrain.
Any "civilisation" that develops out of this would be loosely-organised horse nomads, most comparable to the Plains Indians, ruling over a horticulturalist village culture most comparable to the Pawnee, Arikara, etc. The transition to agriculture for them might occur because of the demands placed on them by trade that occurred between Aboriginal groups, which in turn would be caused by overhunting of the kangaroo and the emu. As we saw in North America, bison numbers declined nearly everywhere after the introduction of the horse, even before intensive white hunting. It's gonna be much easier to kill a kangaroo or an emu when you're on horseback, and sooner or later, you won't be able to sustain yourself, your family, or your tribe, based on those numbers, hence you'll go elsewhere to find more. Depending on how many tribes pick up this lifestyle (and many will, elsewise they'll be outcompeted), this will mean huge declines in kangaroo and emu numbers, and the winning strategy will be to trade with tribes that have more food from other sources. I'd expect because of this that Australia will be slightly more populated in the pre-colonial era, even though they'll still get mostly wiped out by smallpox and other diseases in the long run.
The British or any other would-be colonial power will no doubt find them easy to get rid of, but in marginal regions, they will fight back, and they will be a huge thorn in the side. That goes even more if anyone introduces the camel to Australia and some society transitions to camel nomadism. The village Aboriginals will be dealt with as per history--their numbers will be too small after disease and they'll be forced to surrender. Practically, I wonder if the means of dealing with Aboriginals (more treaties, I bet) as well as the fame they'll gain as expert raiders will mean they can at least move to American Indian status in terms of treatment and perception.