Hum, apparently there are scholarships you can apply for for Masters or Doctorates, with foriegn students needful to be full time students to qualify for scholarship.
With some cursory googling, it appears that astrophysics students are often scholared and part educated through many of the existing astrophysic scientific organisations, such as the Australia Telescope National Facility, in partnership with the traditional education institutions.
Extra travel scholarships of $5,000-6,000 also seem standard for Astronomy PhD students. Probably partly because Aussie facilities are dotted over the whole continent, and partly because some courses offer guaranteed time on overseas facilities such as the 10m Keck telescopes in Hawaii.
At one institution there are two scholarship rounds each year: the main round in late October and a smaller round in late May. That sounds about standard. Aussie school years start in January-February. Second Semester starts in July.
Astronomy scholarship info Maybe calling the nearest Australian embassy would be a good place to start to find someone who will find you fee information.