Be on the safe side. Go to the Australian Webpages to
check on how to register yourself visiting there, as well as
applying for a visa if needed.
Then, if you are Singaporean, go to the Ministry of Foreign
Affairs webpages to check on, and register that you are going
overseas.
And also, if you are male Singaporean, do check with the CMPB
office or at least let them know you are travelling out of
Singapore.
Please print out your itinery and bring it along with your
passport. Cos you may need to show proof that you have a
ticket home at the air ticks and custom counters.