Thanks for using our forums. You have a great question and I would be happy to help you with your questions.
The Slingbox 350 isn't supported for use in Australia, but it should still work. The only issues you may run in to are you provider not being listed (you would just pick any provider since there isn't one for your country) and the virtual remote may not be listed (which you can request a custom remote be built for you on our answers forums). The Slingbox itself should still work though. The link for the custom remote is listed below.
Hope this helps,
The Sling Moderation Team
Probably worth pointing out that requesting a Remote using that method can take months. As a short-term solution there are some Custom ones at http://www.hifi-remote.com/forums/dload.php?action=category&cat_id=87