Welcome to FT. You would have to purchase a ticket for the infant in order to seat them with the car seat. They won't just let you have a vacant seat free of charge, even if there did happen to be a vacant one right beside you. An infant (up to 2 years old) seat is charged at some discount, maybe about 10% of the adult fare or some other rate, so it may be worthwhile buying her a seat anyway, and it would definitely be safer.