The update is being sent out OTA, but for those who can't wait, a hookup to the ol' PC and the use of Samsung Kies will coax out Android 4.1.1 manually. Vodafone's main competitors in the country, Telus and Optus, already offer the LTE enabled Samsung Galaxy S III with Jelly Bean installed, so Vodafone is playing catch up in Australia.
In the U.S., Sprint was the first carrier to disseminate Android 4.1 to its Samsung Galaxy S III users while some T-Mobile customers claimed to have received the update a week and a half ago. A leaked version of the update, believed to be the final build for Verizon customers with the model, was spotted a couple of weeks ago making Big Red's Samsung Galaxy S III owners the favorites to get Jelly Bean next.
source: Vodafone, Ausdroid via AndroidAuthority