A legitimate Australian online casino must:
be licensed by a recognized gambling authority;
have a license confirmation: a copy of the document or a link leading to it somewhere on the webpage (in the footer, company description, or Terms and Conditions)
have good customer feedback;
not be found on any blacklist created by independent watchdogs of the industry;
have a responsive and helpful customer support team.
These aspects are the minimum requirements that will save you from a disappointing gambling experience.