Do you hold an Australian passport? If so, you will have no problems whatsoever. You don't have to tell them you weren't born in Australia. Japan is not so racist as China or Taiwan when looking for native English teachers. As long as you are native (or very close to it) and hold an Aussie passport, there wont be any problem at all.
I bet you can't wait now to get over here. I suggest Osaka / Kyoto / Kobe area. The best in Japan!
