If it were me I would want to at least keep the car seat in the box to have the insulation protecting it from the wrath of the baggage handlers. Having said that, I've checked my children's spare car seat on a few occasions with no apparent damage. Is there anyway you could order the seat online and either have it shipped to their house or pick it up locally upon arrival?

I really think you carrying it on with a doll of some sort would be entertaining. You must post pictures to this thread if you go that route, however.