Cheapest flight I can find for early May (two months from now) is $1200 from U.S. to Melbourne. Is this a good deal or should I keep looking?

From where in the US? We paid $1400 from LAX-SYD and MEL-LAX for a November 05 flight, which went down by about $200 pp about two months after we purchased (bought tix approx April prior to travel, so sale was on approx June??). Never went any lower than that. Just paid $1200 for LAX-AKL and SYD-LAX for right after Christmas which we think is a steal.

Oops, sorry. From Washington, DC.

I guess I thought that since it was not the peak season, the flights might be cheaper. Then again, I'm looking for flights within two months ...

Have you checked the Qantas Aussie AirPass? We went last year in August and the fare from LAX to either Sydney, Melbourne or Brisbane was $999 plus you got 3 flights within the country. The killer, however, was the add-on fare from DC to LAX. If you have some flexibility, you might check out JetBlue for a cheaper fare to the West Coast.

The fares have always been the best from LAX and lots of folks travel to/from LA on FF miles or other low cost options. Air Pacific worked for us for our high season trip - perhaps you could check them out as well since you will travel at low/shoulder season. We will get AA miles traveling with them.