To buy from the Kindle store, you need a Kindle registered to your account and some way of disguising that you are not in the US. See the Kindle forum for more details.
If you don't have access to the Kindle Store, then what you need are DRM-free MOBI ebooks, which can be downloaded to your Kindle via USB (put them in the documents directory). If the ebook isn't MOBI, then use Calibre (has its own forum) to convert DRM-free ebooks to MOBI. Calibre will also "manage" the copying of ebooks to your Kindle via USB if you want.
Many ebooks (but not all) you buy have DRM (encryption). It may not be legal in Australia, but the DRM from all popular ebooks formats can be stripped (see lots of threads here on this), and it is hard to see who is hurt by doing so for personal use on ebooks you bought.
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