Check out skyscanner.com for best deals 4000 seems awful high for a family of 3. We traveled as a 5 piece (2 adults 3 children) for 2200 from Heathrow to brisbane with Eva air. Was economy class but the plane they had, an airbus, meant plent of seat and leg room.
I'd go to a few airlines direct and check out their prices and offer too, some that we've heard of with good schedules and services to Sydney for families are...
You could also check with BA and Qantas but we often find they're more expensive.