I found Jetstar or Virgin to be the best when flying with kids (I mainly use Jetstar). Virgin were very helpful when i flew alone with Chelsea.

I love Tiger for their flight crew..but horrid for anything else and refuse to fly with them again!!

As for getting to and from airport accomodation...bus, taxi.....but def hiring a car with a car seat is sooo much easier!! In QLD we used Europcar and they were fantastic. Made sure the seat was the right way, had the car organised when we arrived. Just made us feel very at ease.