Sometimes is does clear up in the morning. More often I notice it clears up just after sunset. This happened to me recently - it was raining and cloudy all day then cleared at sunset and was clear all night.
Video
Keep an eye on the forcast and look out the window a lot. If you have an all sky camera, you can also get some software to wake you up when it's clear.
This site is also worth keeping an eye on:
http://www.yr.no/place/Australia/Vic..._detailed.html
James