The lack of SMS integration is a perennial complaint for Australian Twitter users. Chime goes a fair way to solving that problem, letting you update your Twitter status via an Australian phone account.
Register your Twitter account with Chime, text the supplied confirmation pin, and then you can update your Twitter account by sending SMS messages to 0429558117. Those show up on your regular feed, tagged as being sent from Chime, and the only cost to you is whatever you pay to send a regular local SMS. (You can also use the service overseas; I did my registration and testing from New Zealand.)
It’s unlikely that Twitter will ever offer receiving updates via SMS in Australia (in the US, where the recipient pays, that’s a more viable model). Until it has its own official service for sending messages, Chime is a great substitute, and much cheaper than the previous alternative of using Twitter’s UK text number.