While stores carry them and people use them all the time, we were told in our very first childbirth class 8 years ago never to use any neck or head support that does not come with the actual seat. We were told it can be dangerous because different seats are made differently, different sizes, etc.
If the car seat was installed properly, her head shouldn't fall too much. Have you had the seat looked at by a police station? The seat should be at a 45 degree angle and 9 times out of 10, needs a towel or foam tube under the base where the seat and back of the seat meet.
My 10 month old's head used to fall to the right but it was usually when his seat was in the stroller. When that happened I would just use a burp cloth, fold it up and lay it under his head/cheek on that side.
If you have any question, don't hesitate to go to your local police department. You may have to schedule an appointment or see if there is an event going on locally like the police sometimes do.
I was just thinking, does she have a headrest in there now that came with her seat? We just moved my youngest to a convertible seat a couple of months ago and his head kept flopping in the car. I knew the seat was in right but come to find out, I had to REMOVE the head rest that goes behind their head.
Best of luck,
L.