Moving from Australia to the US, is there a way to transfer my license in any way, or do I need to sit the exams in full? I'm wondering if there is any concept of "credit" towards licensing, so I wouldn't need to sit all three exams (assuming I was going for Extra).
There is no reciprocity agreement between Australia and the USA, and the US Federal Communications Commission rules for amateur radio licensing and operations also do not provide for any way to get a license except by taking the test(s).
There isn't a way of transferring the credit towards a permanent license. Luckily, the US exams consist of a large degree of practical knowledge. Bottom line is, you should be close to getting the same level of license from your knowledge base. I've periodically taken the tests, and I score higher ever time than I did when I was studying originally, because I have learned through working with Amateur Radio the knowledge included in the test.