I fly between the UK and Australia fairly regularly.
For me, the difference between Economy / Premium Economy and Business Class is huge, largely because of the fully-reclining chair.
I do not find it easy to sleep sitting up, which is only made worse, nowadays, by having chronic muscular aches and pains which can make sitting for long periods very painful. If I'm Business I can sleep really well.
This has another benefit: especially if you choose your flights to land at the right time (the evening at your destination), you can travel in both directions with less and indeed often no jetlag. This requires other strategies (in terms of timing of meals, when to drink alcohol, taking melatonin) but it makes a huge difference too.
Finally, if you just like the fun of Business Class - the meals, the service, hanging out at the Emirates' Bar – then that's another reason to book it. If this is a holiday of a lifetime why not start it on the plane?
My other advice is to try to fly on the A380. A warning if you choose Qantas - they have revamped most of their aircraft, but I think they may have at least one that still has the old skool pod seats that were cutting edge in 2004.
Another option to break up the 20-24 hour flight is by travelling part way (say to Singapore), taking a few days to recover from the first leg and get used to the new timezone, before travelling on. The cost of hotels will likely be much cheaper for a family then travelling in Business.
I am so glad you are heading to Australia, you will love it!