Hazel, all airlines seem to have slightly different policies. When we flew, joshua was 15 months old and he was on our lap, then into a moses basket type thing which was tiny. Otherwise its on your lap for the whole time. We were lucky that we had a 3 year old and a 5 year old too so the 3 of them could fit on the 2 seats.
Night flights are the way forward though as they were asleep within 45 mins of leaving heathrow.
Cathay let us keep buggy up until very last minute and made us priority seating so we were on first. they do that with all families with under 2s.
Im sure most airlines are the same. I phoned Cathay with a host of questions which they answered without getting the hump. They are up to date as opposed to travel agents who dont necessarily know the new procedures of airlines that are changed all the time.
My advice would be to phone Qantas and speak with them