Do I need to apply for a visa if i want to travel to Australia using my US re-entry permit?

If you have a passport, are staying for less than 3 months and do not intend to work and are a US citizen you can enter Australia without a visa as part of the visa waiver programme.

I doubt Australian customs and immigration will be very interested in a re-entry permit, whatever that is.

the above answer is wrong, americans do need a vistor visa to enter australia and a valid passport

http://www.travisa.com/australia/

As Australia is a puppet of the U.S.A., a U.S. re-entry visa will be fine. Just book your return flight for a couple of hours after you arrive. Better still, book one way, and save on the return, because Immigration will pay. You may even get some free accomadation at the Villawood boarding house.

Enjoy your time nearly into Australia