I have flown with Qantas many times, inside Australia and overseas (mainly on long haul flights to Europe) and have never had a problem with Qantas. The people are quite friendly and are cheerful when you make a request of them. The planes feel quite safe, although they do lack some of the other in-flight entertainment that other airlines offer (like the TV screen in the back of the chair). I think one of the most important things though is their safety record, it is excellent. The food is usually good, and they serve ample amounts of beverages (alcoholic and non-alcoholic). One thing that I also like is when you are flying into and out of Australia they show the latest news reports on TV from Australia so you can keep up with what is going on. This is usually more interesting (for me anyhow) than a re-run of Seinfeld that I have already seen 15 times in the past.
I have also taken my bicycle with me from Australia to Europe (to Stockholm via London and Manchester) and had no trouble what so ever with that. They provided me with a box to put it in when I arrived in the airport in Melbourne, I dismantled the bike a little (wheels off basically) and checked it in. They charged me nothing extra for the bicycle, I just had to tell them a few days before the departure of the flight that I wanted to take my bicycle with me. I was extremely impressed with this because it meant I could take some nice trips around Europe with my own bicycle at no extra cost! It all came out in the other end in one piece as well!
I would definitely recommend them if you are considering flying with them. Of the airlines I have flown with I would say that Qantas were one of the best.