I've been to Oz on my own. Apart from sitting in the same place for rather longer, it's not really any different to flying (or travelling by train) between, say, London and Edinburgh. (i.e. the journey itself 'is no big deal').
Advice?
1. if your finances allow for it, try to include a few days stopover somewhere on either the outward or return legs of your journey. (Singapore is fantastic).
2. Again, if your finances allow, try to visit just one other Australian city. (Oz is massive. Unless you've got loads of time and money, two cities will be enough). I strongly recommend Perth. It's the most isolated city in the world (absolutely nowhere near to any other city), with a distinct character of its own, and with some fantastic scenery nearby.
3. Check the weather for your destination city/cities carefully before you go. Oz has loads of lovely weather but you'll need to be prepared (depending upon the time of year) for plenty of rain and/or really high temperatures.
4. Don't make any great plans for your first two or three days in Oz. Your body clock will tell you that it's the middle of the night and you'll be too exhausted to do much. (Equally, give yourself time to recover when you get back!).
5. Relax and enjoy yourself. Even in 'economy' all of the airlines look after their passengers well. (There's usually unlimited free booze - but don't overdo it!)
6. As soon as you've got a specific question, post it here and we'll answer it!
http://gb.sydney.com/
Chris