It is very unusual for mathematicians in Australia to have their own funding for PhD scholarships.
Almost all PhD scholarships are awarded by the University. Most are directly funded by the government or by university money. A small number may be available for applicants from specific institutions or countries, due to special programs or agreements.
Applicants are ranked using a complicated formula that involves, but is far from completely determined by, merit. The result is a score. The cutoff for getting a scholarship is surprisingly high, especially for international applicants, and is not consistent from year to year or even across the two rounds advertised each year.
If you want to apply for a PhD under my supervision, you are really applying to the University. This requires you to get some "in-principle" agreement from me. To get this, you'll need to send me your academic transcripts, your CV/résumé, any theses that you have written, and a specific statement addressing why you wish to work with me (mentioning some specific paper). The more specific and less vague you are, the better.
I need these because I need to judge if you are serious, if you have the background required, and if you are likely to score high enough to have a chance at a scholarship.
I am sorry to say that if you send me a generic enquiry that doesn't help me with this judgement, then I'm extremely unlikely to respond. It's nothing personal.