I'm going to have to balk at that 1901 rule for a simple reason.
In my opinion, one of the reasons why Australia is so stable and peaceful compared to it's neighbours is that it was at first colonized by a culturally-singular racial group and then it was settled by the British Empire, the most powerful and economically stable empire at that point in history. Another factor that plays into Australian stability is that the Aboriginal tribes were not actual kingdoms or nations. This allowed the British to easily colonize the continent, without any worry of controlling native empires or nations. This has prevented Australia from having something like India's caste system or in fact, India's wide-ranging cultures. This allowed the future Australia to have economic stability and cultural stability, since most white Australians in the early 1900s were Christians and the Aborigines were effectively pushed into minority status.
Not just that, but the British Empire mostly left the Australian colonies alone to run their own affairs, unless it involved military matters or foreign policy. (Each of the Australian colonies had to get the permission of British Parliament to form their own defence forces). if Australians did revolt, it was against the authorities appointed by the British, not the British themselves. Just look at the Eureka Rebellion and the Rum Rebellion.
I don't want to say this made Australia destined to be successful, but it's a important element to consider. So, if you want to turn Australia into a hellhole, I would suggest the country being colonized by multiple countries, most likely ones who had a terrible record of governing their colonies (looking at you, Spain). Just look at how Spain governed Latin America before it's wars of independence. Spain's governorship of the colonies created strong racial and national divisions that prevented them from coming together to form a stable and long-lasting Gran Colombia. I'm not saying early Australia's treatment of Aborigines was good (New Zealand didn't want to be part of us for that very reason), but it could've been far worse.
Another alternative POD I can think of is for many primitive cultures, not just Melanesia/Papuan-descendant Aborigines, to colonize Australia. Opposing cultures could force the Aborigines into forming their own nations or kingdoms, to fight against common enemies. This would have a domino effect across the continent, with the other primitive cultures forming their own kingdoms or nations. This could make the European effort to colonize Australia more difficult and force them to engage in diplomacy, which could slow the rate of European colonization, potentially making white Europeans the minority and Aborigines the majority. This could force Australia to wind up like South Africa, with a majority-black government ruling over a minority white populace, against which there is the occasional hate crime and the occasional government-backed land grab.
(I am not pushing the white South African genocide nonsense. Farm attacks in South Africa are part of a wider crime problem and are not limited to whites)