We flew with virgin blue with bub at 10weeks. They were really god with us, and we had two flights up two flights back. I'm not sure if you would get the bassinet, I know you do on international flights, but they just have bub on your lap with an extra seat belt.
You can hire baby car seats through car rentals, it cost us $ 8 for a day, but I'm not sure about it if you are using a friends car. Do you have the option to take bub's seat? Infant luggage isn't counted generally