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For interested Aussies, you can enable the service by sending the text message "START" to 0198089488. Associating your phone with your Twitter account will enable all the usual Twitter text commands.
This adds Australia to the list of official countries supporting tweets via SMS: United States, the United Kingdom, Canada, India, Indonesia, and New Zealand. Waiting for your country or carrier to be supported? Twitter's blog post says to sit tight for more announcements coming soon.