The radiant of the Geminid meteor shower above the northern horizon as seen from Adelaide on the morning of December 15 at 3:00 pm ACDST, similar views will be seen from other sites at equivalent local times.
The Geminid Meteor shower is at its peak from the point of view of Australian's on the mornings of Wednesday 14 December (13 December UT) and Thursday 15 December. The best time to observe is between 1 and 4 am (daylight saving time, 12-3 am non-daylight saving time), with the highest rates between 2-3 am daylight saving time.
The Moon will unfortunately be just above the Geminid radiant, so only low meteor rates will be seen. In Australia we should see roughly a meteor every 6 minutes.
You can check predictions for you local site with the NASA meteor flux estimator (scroll down to 4 Geminids in the SHOWER box, make sure you have your location and date correct as well)..
Printable PDF maps of the Eastern sky at 10 pm ADST, Western sky at 10 pm ADST. For further details and more information on what's up in the sky, see Southern Skywatch.
Cloud cover predictions can be found at SkippySky.