>>> "Won't I need an extra ticket to bring the carseat??"
Only if you plan to use the seat on the plane. You can carry the child to the plane in the seat. If seat can not fit as carry-on then they will store it for you. When getting off plane they give seat back. Same process as if you have a wheelchair. Yes, some buy a seat for a child but not required if under a certain age. You still need a plane ticket for the child since International Travel. But you are not charge for a seat since not using one. Just tell Travel Agent you have a child age # months. You might be charged some taxes if I remember from 10 years ago.