From my experience the best time is between 2am to 4am. You may get a few earthgrazers from around midnight onwards but its not common. Generally you don't get meteors unless the radiant is above the horizon. Leo doesn't rise until mid morning for us. Also, you start to get twilight from 3.30am onwards and by 4am its usually gotten too light to see anything.
Weather forecast for Wed morning is not that good for Perth, so I'm not getting that excited about it. Most Perth amateurs know that a "Leonid storm event" is usually a meteorological event, not an astronomical one!