This isn't really related to cakes but just because your daughter's birthday is not technically during your trip doesn't mean she can't have a button, especially if this trip is for both of them. If I was your daughter I would be kind of upset because even though the trip was supposed to be for both, my brother would get treated extra special while we are there because everyone will be telling him happy birthday left and right while he is wearing that pin. Just IMO. So if the only thing holding you back from birthday pin, noted on reservation, etc. for her is the actual
date of her birthday, Disney doesn't care and there is no reason why she shouldn't get one too.