Please see my earlier post from 2009 for some good advice and suggestions on the cheapest and best ways to get to Australia.
I went to Australia for two months this year and flew Qantas from LAX via New Zealand. It was a long flight but I enjoyed the free stopover in New Zealand for three days on the way back.
Also, for no extra cost, we flew into Brisbane and made our own way to Cairns where we flew out. We did the entire trip with all these changes and stopovers for under $1000 each.
I still don't like Qantas but end up using them almost every time now due to the flexibility they offer with the cheap fares. The service isn't the best. In fact I would say it is actually quite bad. I would choose Air New Zealand any day, except they just can't offer me all the options I need.