Compatibility summary
You will need a travel adapter in Australia; plug types used there differ from Singapore.
Plug comparison
Singapore plug types: G
Australia plug types: I
There is no common plug type between Singapore (G) and Australia (I). You need a travel adapter.
Voltage comparison
Singapore: 230V, 50Hz
Australia: 230V, 50Hz
Voltage difference is within a range many devices tolerate; check your appliance label.