Here is what happen to me on our last trip. Maybe someone can help expalin to me what I should do if this happens again, but from my past experience, buying a seat for an infant, one you would want in a car seat, may be a waste of money and here is why.
All of my kids were over 2, so Ihad to buy them all a seat. I decided I wanted to keep them as safe as I would in a car, and brought along their car seats. I had a 2 year old and a 4 year old. The 6 year old was good in his own seat. We checked in early enough, but was told we did not have a window seat for the one of the car seats, and due to safety regulations ALL car seats have to be strapped to a window seat. ( the plane had 3 seats on either side of the aisle) I asked if they could just move someone to the aisle seat and assign my dd the window seat. No, they could not do that. But I could ASK someone to switch seats once we boarded. Well, what if they are not willing to switch seats? Then you can't use the car seat, you will need to have it stored with the strollers underneath. This BURNED me because on more than one occasion, I have gone to the airport with pre-assigned seating, only to find out at check in that those seats were given to someone else. So, why is this any different? I had been moved before, I was one of the first in line to check in, so I am sure they could of found a window seat for the car seat. ( should I have been more aggressive and demand a window seat?) Well, they flight down was OK, because when we got on the plane, the woman who had the wondow seat was already there, I explained how I needed the wondow seat for the car seat, she was more than willing to switch to the aisle seat. ON the flight back, same thing, I was not assigned to a window seat for the car seat. (dh, and 2 ds's had the 3 seats across the aisle, again they were all set) I started to strap the car seat to the window seat, and my dh asked why I was doing that, because the person the seat belonged to was not here yet, I said, geesh, who would NOT switch seats? The other lady switched no problem, what is the big deal? He convinced me to wait, and when the woman arrived, I didn't even have the full sentence out of my mouth to ask her when she cut me off and just said "no, I am not switching seats"

I was speechless!!! There wasnothing I could do but to bring the carseat up to the front and have them store it with the strollers. SO, my dd sat in a big seat with her tiny body strapped to a BIG seatbelt. I was so upset. Who wouldn't switch??? The woman later explained to me that she is afraid of flying, and is supersticious, she will not change her seat once her seat has been assigned. I wanted to scream at her.."why??? because you are afriad that is we crash, the person in your original seat will survive and you will die in the newly assigned seat???" WELL, I have a huge problem with that because she was basically saying she would rather save her own butt than a 4 yo little girl's. Not to mention, she could survive in any seat, she was handing my dd a death sentence by not allowing her in a car seat. I wanted to tell her what the chances are of ANYONE surviving a plane crash, but I am not that mean. LOL
SO, BEFORE you get to the airport for check in...check on your seat assignments and MAKE SURE you have a window seat for the car seat. And make sure it is written in stone.