A vast country, in fact the only nation in the world that is at the same time an entire continent, and chock-full of all manner of tourist attractions, especially of the nature and scenery type. The major cities of Sydney and Melbourne are also prime tourist draws.
As far as dark tourism is concerned, however, Australia isn't in the top league of countries. There are only a few sites that I am aware of – although I admit readily that this may also simply be due to me not having done sufficient research into this.
What I do know about includes these specific (partly) dark historic places that are well developed for tourism:
One could argue that maybe Uluru (formerly known as Ayers Rock, but meanwhile re-re-named politically correctly to its Aboriginal label) could qualify as a sort-of dark site too. Its very size, the specific light, the whole mysticism surrounding the rock (the largest monolith on the planet) generates a somewhat spooky aura, many feel. I'm not sure, though, that this is "real" enough to make it a dark tourism site proper (see the concept of dark tourism and beyond dark tourism proper).
However, there also was a very real high-profile crime case that involved Uluru, when a baby named Azaria Chamberlain disappeared there. The parents were put on trial and the mother convicted of murder, with much dubious media fanfare surrounding the case. Several years later she was released and acquitted when new evidence came to light. The most widely accepted story today is that the kid was indeed snatched by a dingo (as the mother had claimed all along). Obviously, there isn't a specific site linked to this story commodified for tourism. But the case, which has also been adapted into various media forms such as TV, movies and music, may be regarded as lifting the dark elements of Uluru into the non-esoteric modern world too …
Australia has suffered numerous very real-world, natural disasters, especially in recent decades, including devastating bush/forest fires, floods and droughts, though I am not aware of anything commemorating these in a form developed for (dark) tourism. Voyeuristically inclined travellers may well still encounter evidence of the destruction caused by fire or water when passing through the relevant areas.
Australia does have an unequivocal modern man-made dark legacy as well: it used to be the chosen place for British nuclear testing in the earlier phases of the atomic age. Thus the very first British atom bomb was detonated at the remote site of the Montebello Islands off the west coast of Australia. 
The main nuclear test sites in later years of the 1950s, however, were inland, on the edges of the Great Victoria Desert, namely at Emu Field and Maralinga in South Australia.
Apparently, these latter places can now be visited too, though it is not quite clear in what form. The areas have (allegedly) been cleared up – and handed back to Aboriginal communities. So it may be necessary to make arrangements with them when planning to go there. It is also not quite clear whether there is anything much to see there. I've seen pictures on the Internet of a sign marking the Marcoo Site (though I don't know how accessible this may be). Other than that you may only be able to see the empty open expanse of the desert and will have to use your imagination to link the place to nuclear tourism …
What Australia undeniably has in abundance is ghost towns in the "Outback", often abandoned mining sites. One particularly controversial and sinister place is Wittenoom in Western Australia, a former blue asbestos mining town (cf. Asbestos). It was abandoned over (very valid) health concerns and today the official government line is that you should not visit the place (it has even been taken off maps, and road signs mentioning the place have been removed). There are certainly lots of less sensitive abandoned places and ghost towns – but I'm just flagging this up here, without going into any more detail … as yet. I may do more research on this – and other aspects of Australia – at some point in the future, though, so do check back …
Other candidates for future inclusion may be a couple of Australia's open-cast mines or further ex-convict-colony-related places. One could argue, too, that Australia may even be one of the very few countries in the world where wildlife observation can count as something dark (cf. Komodo) – given that nowhere else on Earth are there so many extremely poisonous animal species, some of absolute overkill capabilities. In general, however, Australia's wildlife and scenery are not considered dark tourism as such, but they are certainly what attract many of the foreign visitors to this country.
As for travel to the country in general:
Getting to Australia takes time (unless you're travelling from New Zealand or Indonesia), and for most of us costs a pretty penny too. Getting around in the country can also take up a lot of time, given the vastness of the continent, though for the dark tourist not the whole vastness of the place is relevant, of course.
The tourism infrastructure in Australia is usually excellent, except, naturally, in very remote areas, where it gets significantly more adventurous (which is part of the appeal to many Australia tourists!)

©, Peter Hohenhaus 2010-2018