From the late evening of the 28th November to the early morning of the 29th November there will be a penumbral eclipse of the Moon. It will be visible in all of Australia, New Zealand and most of Asia.
In a penumbral eclipse, the Moon only enters the outer part of Earth's shadow. This will results in a subtle darkening of the Moons northern half (although it is a relatively deep penumbral eclipse, it still doesn't get very dark). Depending on how good your eyesight is, it could be reasonably visible, or only visible via photography.
The table below shows the time of the eclipse from Eastern, Central and Western Australia. For Eastern and Central Australia subtract an hour for non-daylight saving states. The early parts of the eclipse will be effectively invisible to the unaided eye. When around 2/3 of the Moons disk is immersed in the penumbra, then you will see an effect (around half an hour either side of maximum eclipse).
|Penumbral Eclipse Begins||Maximum Eclipse||Penumbral Eclipse Ends|
|11:12pm AEDST 28 Nov||01:33 am AEDST 29 Nov||03:53 am AEDST 29 Nov|
|10:42pm ACDST 28 Nov||01:03 am ACDST 29 Nov||03:23 am AECST 29 Nov|
|8:12pm AWST 28 Nov||10:33 am AWST 28 Nov||12:53 am AWST 29 Nov|
For everywhere in Australia except WA, the eclipse occurs around midnight, you will have to be dedicated to stay up for this. For other regions, see here for UT timings.