If you are younger, then you will likely pick up a new accent very easily. If you are older, you may need to train yourself... mimicry (it is very possible with some effort).
"How long" it will take for you to pick up an Australian accent is really variable. General American and Australian share most of the required English phones; if you have knowledge of phonetics you can easily learn to pronounce individual words like a native speaker. However, only through constant (effortful) mimicry will it really become embedded in your speech.
(There is no scientific evidence to suggest that people "can't" pick up accents, dialects, or languages after a certain age. It is certainly more difficult, but there have been far too many effortful counterexamples.)