I've flown a bit with both kids on my own and aside from the meal, I really haven't found much difference between Qantas and the others - except Tiger, they suck.
I've never had a bassinette though, it def depends on the size of the aircraft and often if you're travelling alone they will give those seats to able bodied passengers who don't have someone to look after (just in case there's an emergency - well that's the line they often feed to me anyway).
I've never been charged for anything infant related as luggage, though making sure you can manage all the paraphernalia and DS is the challenge. I rarely fly with a stroller for example and use the sling when travelling, as it's just easier.
Car rental places won't hire the carseat without the car, but there are plenty of baby hire places in capital cities if you do a search. Usually installation is up to you though.
If you do hire a car, many will now get you to install a babyseat yourself as they don't want to be held accountable if it's wrong IYKWIM?