I thought that travel visa was only good for 30 days, so they might not have any rules with 6 months on passport.
You can enter and stay for 90 days without a visa.
You should be fine so long as your passport is valid for more than 90 days from intended entry.
From the State Department's web site (linked below):
ENTRY / EXIT REQUIREMENTS FOR U.S. CITIZENS: You must have a valid U.S. passport and a visa to enter Australia. Most U.S. passport holders traveling to Australia for tourism or business purposes for less than 90 days can obtain an Electronic Travel Authority (ETA). The ETA is an electronic label-free visa and can be obtained at the ETA website for a small service fee. Airlines and many travel agents in the United States are also able to apply for ETAs on behalf of travelers. If you overstay your ETA or any other visa, even for short periods, you may be subject to exclusion, detention, and removal by the Australian Department of Immigration and Citizenship (DIAC). You can find more information about the ETA, other visas, and entry requirements from the Embassy of Australia at 1601 Massachusetts Avenue, NW, Washington, DC 20036, via the Australian Visa Information Service at 905-280-1437 (toll charges to Canada apply) or their website.
visited the web site until now. It looks like the ETA is valid until the passport expires, and as long as the ETA is valid, travel is permitted.