Not really sure what you mean by 'perks', other than a Guest of Honor badge (which I think is free). My understanding is that a Guest of Honor badge may get you some Happy Birthdays from CMs and special attention from characters, but I think that is it.
I think you would do better to plan something special to honor her birthday if you so choose, but as the mother of a DD9, I would hesitate to stretch the truth and act as if her birthday is while you are actually at WDW. Maybe a special meal, a new outfit, or a really great souvenir.
I just don't feel that it is honest, and would not want to impress on a child that it is better to mislead someone or stretch the truth to get better treatment than others. After all, we all have a birthday at some point during the year in which we vacation at WDW, what would they do if everyone expected such treatment.
Prepared for flames, but sticking to my guns on this one.
***If I am wrong about perks available to GoH wearers, please let me know, our next trip is in September, and will include the actual day of DD and DH birthdays.