Yes, you can do the same here in Oz. Telstra, Optus, Vodaphone and 3 are the big players. You just buy a prepaid Sim. Optus and Vodaphone seem to offer the most flexible deals. I use Optus, Telstra has the best coverage but you pay a premium compared to the other providers.
www.optus.net.au
www.telstra.com (or
www.bigpond.com - same "company" different branch)
Cheers