When travelling with Maddy I swore by Virgin Blue. We've flown the Brisbane to Sydney route since she was 9 weeks old and I always found them very attentive and helpful. If you're flying with an infant (under 2), you can use your pram in the airport and drop it off at the boarding counter a few minutes before you board. They usually give you priority boarding (along with those who need assistance) and they tend to reserve the back few rows for the parents with children.

Did Jetstar once (Bris to Newcastle) and it was was a red-eye early flight but went smoothly. Haven't done Qantas yet with Maddy, but we will just before Christmas when we go home to see family.

You can travel in Qld in a taxi holding your child under the age of 2 in the backseat as Falguni pointed out. Not recommending it, but I know Ive been in a spot before where there haven't been any available taxis with carseats and ours has been with DH in the car at work - I did the HAB thing as well.