Yes you can apply for the US visa from any US embassy abroad even if you are on a visit visa. It may be harder but it is possible. According to the US embassy in Canberra:
Q: Can I apply for a visa in Australia if I am not an Australian passport holder or a permanent resident here?
A: An applicant has the right to apply for a nonimmigrant visa at any U.S. consulate abroad, therefore you can apply at any U.S. consulate in Australia.
However, it may be harder to qualify for a visa when applying outside your own country of permanent residence. At your interview you will be required to demonstrate that you have strong ties abroad, and that you will return overseas after your visit to the U.S. If you choose to apply in Australia, keep in mind that your application may be refused, and the application fee is non-refundable.