What passport are you holding?? Unless you hold a passport/travel document of the 38 countries listed on
ICA website, you won't need a visa to enter Singapore.
Regarding Australia visa, it also depends on what passport you hold. It may or may not be free, depending on what visa/ETA you are required to apply for.
https://www.border.gov.au/Trav/Visa/Appl/Visitor