Singapore would usually allow you to bring through your purchases, but since your final destination is Australia, you're out of luck. From the Changi Airport FAQ:

Q8.If I am transferring or transiting at Changi Airport, will my liquids, aerosols and gels items purchased at other airports be accepted at Changi Airport? Will I be allowed to bring these items onboard my flight?

Passengers (*except those travelling to Australia, the US or on Northwest Airlines or United Airlines) will be allowed to bring liquids, aerosols and gels items in containers larger than 100ml onboard their flight if these items are placed in sealed tamper-evident bags with the receipt clearly displayed in the sealed bag. The receipt must show the date of purchase, item(s) purchased, name of the shop and the name of the airport.