When would be the best time to purchase a airplane ticket from Australia to America?

Right now Iluvafrica, it's going into the North American Fall, that is classed as the low season. So anytime from now on for the next five months. If you book early with airlines like Qantas over there, they do advertise discounted fares.

On one of my trips to Sydney I flew United, and I was very disappointed.

HND

Wait until the end of the school holidays, be flexible with arrival ports, days, times and airlines. Check out stop overs in Auckland, Fiji and Hawaii. Often midweek is best to buy and to fly. It is cheaper to buy a return.