A post in March indicates that it is QFF points; but knowing the class of travel is important.
The watchword,
dvschem is flexibility! For instance (these are mainly relevant to much rarer business class seats, but also apply generally, especially when you are looking for 4 seats):
* Be prepared to consider different departure and arrival ports; SYD/MEL bring American and other Qantas flights into play; LAX and SFO similarly;
* Look at routing that isn't direct - Qantas only services YVR in Australian winter and summer; during those times, and other times routing on Cathay Pacific via HKG would come into play;
* Book as soon as you can; booking as two one-way trips might be necessary IF the return journey is outside the booking window (I THINK with Qantas its 353 days before departure - but some-one will confirm or correct, I hope)
When you say 'how to achieve' ... with QFF points, its just a matter of going to the web site, choosing classic award search and seeing what's there (also being flexible with dates) and booking. If you have plat or P1 status (and maybe Gold also??) with QFF you can also call and request the release of an Award seat if there aren't enough showing on the day/flight.
Be aware that if you are looking at economy, Qantas charges substantial cash charges for a points seat. You can see these by making a dummy booking. It may be worthwhile to book the kids with cash on a cheap fare (if available) as this may not be much more than the extra cash costs with a points flight; then, also you wouldn't need 4 seats on the one flight (but again, with Y 4 seats may not be that difficult - I don't know). The charges for business are also substantial, but for the better experience, it doesn't hurt so much

.
Booking economy (only certain fare types qualify) and then thinking of applying for upgrades with points is very risky and a low probability thing.
This will take time; get to learn the routes (we can help) and just search combinations on the booking page; but equally do it as soon as you can.