Morning sky looking north-east as seen from Adelaide at 5:00 am local daylight saving time on Saturday November 19 showing Mars near Regulus and the Moon, with the Leonid Meteor shower radiant indicated with a cross. Similar views will be seen elsewhere at the equivalent local time. Click to embiggen.
On the morning of Saturday November 19 the Leonid Meteor shower peaks (from the point of view of Australians, that's 18 November UT), with the best time being between 3-4 am.
Unfortunately, the Leonids radiant is just below the last quarter Moon, so very few meteors will be visible (maybe one per hour). You can use the Meteor Flux Estimator to get a prediction for your location. Use the 13 Leonids option and don't forget to set the year to 2011.
If you are going to have a look, be sure to let your eyes adjust for at least 5 minutes so your eyes can be properly adapted to the dark. Don't look directly at the radiant site, because the meteors will often start their "burn" some distance from it, but around a handspan up or to the side.
Make yourself comfortable, choose an observing site that has little to obstruct the north-eastern horizon, have a comfortable chair to sit in (a banana lounger is best), or blankets and pillows. A hot Thermos of something to drink and plenty of mosquito protection will complete your observing preparations. As well as meteors, keep an eye out for satellites (see Heavens Above for predictions from your site). The sky will also be particularly beautiful, with the constellations of Orion and Taurus gracing the north-western sky.