You can't avoid jet lag, but you can work it out of your system quickly. Sleep if you can on the flights. When you get to Oz, do everything on Australia time. Eat breakfast even if you don't feel like eating. Jet lag is not just about sleep, it's about your whole body clock, so eating at normal times will help.
DO NOT NAP! In those first few days you'll be exhausted, but don't nap. Go outside, go for a walk, go shopping - do anything! But do not sit down on a comfortable chair or bed!
Stay awake on the first day until (ideally)9pm Australia time. It'll be tough, and you might not make it, but stay awake as late as you possibly can. 7pm at the absolute earliest for bed.
If you wake at 4am, don't get up and watch tv, eat or anything. Stay in bed and try to doze. If you wouldn't eat at 4am normally don't do it there.
If you can do all that on your first day, it'll be easier on the 2nd day. I've been flying back and forth to Oz for the last 17 years. I know it's heard but it will get better and you'll enjoy your time so much more.
Good luck!