I would check the airline's website (or call their customer service) to check the size of their seats. I believe that most (if not all) Britax car seats are airline certified, so I imagine that means they are going to fit in the seats.
I would try to gate-check the car seat (if possible) not send it in to the hold as luggage as it may be damaged. If gate-check is not possible, you may have to buy a seat for you baby :(
Also, I saw the gogo Kids travelmate that seems pretty handy and might be useful - it's a lightweight wheeled contraption to put your car seat on and essentially turn it in to a stroller!
Product description:
The gogo Kidz Travelmate is a convenient and safe attachment for a variety of convertible/toddler car seats. Instead of carrying your car seat and child through an airport, they can now be wheeled through a crowd!
The gogo Kidz is easily mounted or removed and it allows one hand to be free. It features 5” razor wheels and telescopic handle, and weighs 5 lbs. The quick release wheels provide extra clearance for storage and smaller x-ray machines.