Try to get experience (internship) in your own country of residence first. For example, all the top-tier banks in Australia have very strong Asian franchises in Hong Kong and some in Singapore. If you can get relevant work experience there then I think employers will be more likely to sponsor you here in Australia.

Just to further back up your answer, Ian. I actually know somebody from Singapore who graduated with a Commerce degree last year. He secured a paid job for the superannuation period with Dixon Advisory without actually having acquired Citizenship or anything like that at all. He did sit on a very impressive academic average and a a CV that covered a couple of internship programs he did with MNCs outside Australia.