You're going to LOVE this trip - Walter and I did it in September last year, and it was amazing.
Airfare - Qantas and V-Australia are your best bets. I regularly find round trip coach for under $1000 - but I'm always looking at September, not June (I have nights where I just obsess about wanting to go back there - it's really beautiful). V-Australia is really aggressive with their pricing - they're trying to make a dent in Qantas stranglehold on that market.
I'm not sure if this is still the case, but last September we flew Qantas and booked premium economy. The route from Los Angeles to Brisbane doesn't have a premium economy section, so we were put in business class instead. When I asked why, the flight attendant told me that V-Australia was offering business class to Brisbane for the same price Qantas was charging for premium economy (for us, it was about $2800 round trip per person). I can't begin to tell you the difference it made on the flight down. These were the 'lie flat' sleeper seats - pure heaven.
Also, be prepared - apparently everything in Australia will kill you. Disney was meticulous in warning us about every type of critter, bug, snake, spider, man-eating-plant. Of course nothing bad happened, but they warn you about these things A LOT. Even still, it was a flawless vacation - and one that I would do again in a heartbeat!
Pete