Can I use my iPhone 4s (jailbroken to unlock) in Australia? I have an Irish iPhone 4s already jailbroken for Italian Vodafone. I must use the iPhone 5 SIM with an adapter and the phone works only with my Italian SIM.

Now I am in Australia and I would like to unlock and use it with my Australian SIM! Is it possible? Do I need a new jailbreak?
if your iPhone is already unlocked (e.g. jailbroken and ultrasn0w installed from Cydia) then you don't need to do anything. Just put in the SIM you want and it should work.