Constellation of Leo as seen at 4:00 am daylight saving time 0n the morning of November 18. The Leonid radiant is near the centre of the sickle of Leo, just to the left of Regulus.
The Leonid Meteor shower is at its peak form the point of view of Australian's on the morning of Thursday 18 November (17 November UT). The best time to observe is between 3 and 4 am (daylight saving time, 2-3 am non-daylight saving time).
Despite the sky being Moon-free when Leo rises there will be very few Leonids seen from Australia, maybe 2-3 per hour.
You can check predictions for you local site with the NASA meteor flux estimator (scroll down to 13 Leonids in the SHOWER box, make sure you have your location and date correct as well).
If you are up that early anyway, looking at comet 103P Hartley, look to the east, you may see a couple of interesting meteors, but nothing spectacular.
When you get up, allow at least 5 minutes for your eyes to adjust, and be patient, it may be several minutes before you are rewarded with you first meteor, then a couple will come along in quick succession. Choose a viewing spot where you can see a large swathe of sky without trees or buildings getting in the way, or with streetlights getting in your eyes. The darker the spot the better (but do be sensible, don't choose a spot in an unsalubrious park for example).
A lawn chair or something similar will make your observing comfortable (or a picnic rug spread on the ground and a nice pillow), and having a thermos of hot coffee, tea or chocolate to swig while watching will increase your comfort. (Here's some hints on dark adaption of your eyes so you can see meteors better). Don't look exactly at the radiant spot, but look a bit to one side.
The meteors may be disappointing, but with binoculars you can see a (very dim) comet, the skuy is beautiful and Saun and Venus will rise towards the end of observing time. So you will still have a nice time.
Cloud cover predictions can be found at SkippySky.