Yes, you will need a visa for your vacation in Australia. You can obtain a visa at the Australian embassy, or even access the process online. You can also contact the immigration office for visa rates and extended stay information.
Here's the link.. http://www.usa.embassy.gov.au/whwh/Visas_and_Migration.html be careful because last year when I went I googled a place to get my visa, which took me to a website that said they gave visas out to go to Australia, I payed, waited and never got it.. Thankfully I found out in time that they were a fraud to send all my papers to Washington and they sent me my visa. Good luck and enjoy your trip!