Do you mean stop over as in stop, spend the night, and then catch a plane a day or so later, or stop over as in get off the plane, sit there for a couple of hours, get on the next plane ands continue on your merry way?
Because if you want to stop and visit, then just choose somewhere you want to visit for a few days.
Otherwise, just choose the cheapest and most convenient flight for when you want to travel.
I've flown to Australia with BA, Qantas, Singapore, Cathay and Malaysian and generally they're all much of a muchness. Flying emirates next time.
Most flights are out of an evening, and land in Australia in the morning. A longer second leg can help you get some decent sleep before you land, doesn't work with kids though. If you choose BA or Qantas you can include the Sydney to Perth trip in the same booking and you get less arguments about luggage allowance as they will recognise the international limit on domestic flights. If you book a domestic flight yourself, they won't necessarily do that. A longer layover can give you a chance to let little ones run around.
Only caveat is that Singapore and Cathay are brilliant with children, but have less selection of food etc for young ones, but really lovely toy/ entertainment bags. Malaysian was dire with things for children when we flew, but they had only just joined the One World Alliance so hopefully its improved since then.
Also, if you have a child too big for a cot, but too small for their own seat, BA were the only ones to have a sky cot for them so they don't spend the whole time on your lap. But it has to be a BA plane, rather than just a BA code. They code share so you have to really check whose plane it is.