Three kids, two adults and a desire to see Australia. Sounds simple doesn't it?
Before you go
When planning your budget you need to know that kids (up until 12 years of age normally) travel for about 60-80% of an adult airfare. Kids under two can travel cheaper as long as they do not occupy a seat, something that you really have to consider wisely before undertaking such a long journey.
You also need to make sure that when you get your tickets that the names match the passports for all kids and that their ages are also correct. Most Danes will need some type of electronic visa too, which most travel agencies will organize... However, you have to check these things carefully as last time I was in Australia, one of the visas was not ordered which resulted in all of our bookings being cancelled and rebooked at the airport, as a result we were forced to sit all over the plane. Again for a long trip it just adds a level of difficulty that is not needed.
We travelled with kids aged 5, 7, 9 and they coped with the flights without any problems. Most larger airlines have in-seat entertainment that manage to while away most of the hours.
Some people like to do the stop over in singapore, Thailand, Hong Kong or whichever country you carrier schedules a stopover in. For me, it is not worth the hassle of checking baggage organizing transfers, etc etc. If the kids can cope with it, I can cope with it too.