If your laptop cannot finish the job, the computers you can actually get in Australia fall into three buckets. You do not need to learn the acronyms first. Pick the bucket that matches your login, then use the three-click finder for a plan.
Free instant / 1–2 days
A .edu.au login opens Nectar, the research cloud shared by Australian universities, and often a machine that lives on your own campus. Without that login, Kaggle still gives you a free notebook and about 30 GPU hours a week. Hugging Face ZeroGPU is only for a short demo.
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Students and university staff can apply for Google Cloud and AWS research credits. Independent researchers look at Google TPU Research Cloud, which does not require a university email. Microsoft Founders Hub and NVIDIA Inception are for companies, so skip them if you do not have one.
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Merit grants, or rent by the hourverify
Gadi at NCI and Setonix at Pawsey are the national machines. The usual door is a university merit grant such as NCMAS. If you need a GPU tonight and nobody has approved you, rent an hour and turn the machine off when you stop.
Big jobs, or a paid hour to fill a gap
You can still do the work. The national supercomputers usually want a lead researcher at a university or a research agency. Until you have that collaborator, use the independent path: Kaggle, TPU Research Cloud, and a rental if the free notebook is too small.