Can Kiwis studying in Australia get any financial assistance? Or am I on my own?

You need to be an resident to qualify for most assistance. As an NZ citizen you qualify for a Commonwealth supported place at most unis (some don't have them) wherein the government subsidise the fees. But unless you are a resident or citizen in Aussie you don't qualify for an allowance or government loan. And I don't think Studylink helps unless you can prove that you are doing overseas study as part of a NZ degree (i.e. if you plan to live in Australia permanently or graduate from the Aussie university, Studylink in NZ doesn't want to know you)