Thank you, it's just a leg pillow that goes up to the height of the seat. I think based on my call with them, it isn't permitted, but they gave it just based on size of personal item and that is sort of silly, since it is inflatable object. But anyways, I emailed one of the companies and they said that officially BA is a no but they still receive lots of photos from people on BA with such pillows. I don't want to risk it though, too much of a gamble.
FYI we have a window seat, so it's not at all a safety issue.
I'll stick with a carseat.