I write this post with some reluctance. While the Perseid meteor shower is one of the most regular annual meteor showers and produces 100 meteors per hour (under ideal conditions), it is best viewed from high Northern hemisphere latitudes.
According to the International Meteor Organisation, the Perseid meteor shower will peak between 11.45 pm AEST on Monday 12 August and 11.45 am AEST on Tuesday 13 August 2013. I have produced the above finder chart highlighting the constellation Perseus from which the meteors will appear to originate from (hence the name of the constellation) on the morning of Tuesday 13 August 2013.
I can’t say how many will be visible from mid-Australian latitudes. In theory, not many given that the Earth’s atmosphere will have absorbed most of the dust particles before they could arrive over Australia. If you are an optimist, I would suggest looking between 2 am AEST and the start of twilight on Tuesday 13 August 2013. Note that any meteors seen will appear to come from Perseus. You actually maximise your chances of seeing Perseids by looking away from the constellation.