car seats are generally alot harder and complicated to fit on an aircraft seat and have to be a specific type too, i dont believe they can be booked online anyway, for a long flight i would say yes go for that but its such a short flight its not worth the hassle, the cabin crew are very helpful and will make sure mother and baby are comfortable for the flight, if the car seat doesnt fit correctly and secure, it will be offloaded into the hold and u will lose that money, so from experience as ezy cabin crew and a father, its so much easier with baby on lap, so i would phone customer services any time, and its a flat fee of £20 even if u book on the day
you should at least get a spare seat next to you anyway if you go towards the rear of the aircraft, at the front everyone wants to sit on eachothers laps!
hope this helps