T.H.
I would check it. At 4 she doesn't really need to be strapped down (like say a 1 or 2 y/o might, cuz I've done it! ;) and it's bulky and hard to maneuver through the aisle, etc.
You can check it for no charge, but just know that most airlines will make you sign a waiver that says they aren't responsible for damage, etc. I haven't had a problem until this last flight when my daughter's booster was completely destroyed! They went ahead and replaced it anyway b/c it was a bit extreme! Southwest rocks!! :) But I've done it quite a few times and never had a problem until now.