Andrea,
I just
answered a question along the same lines. The bottom line is this, you should celebrate the birthday during your entire trip!
The celebration buttons are not something that require some proof of birth date. Instead they are there to help people celebrate special occasions as they best see fit. As I told Bruce, when we go to Walt Disney World we are never there on the exact dates of our daughter's birthdays, but they wear their buttons all trip long. You should too!
Remember to also note that celebration on your dining and resort reservations.
BUTTON TIP: When you are requesting the button from your resort's desk, or Guest Relations in the parks, ask them after they write the name on the button if they could put a piece of tape over the name. The marker writing has a tendency to rub off, and this keeps that from happening.
If you are picking up the button from a theme park, make sure you go to Guest Relations after you have entered the park. The lines are typically shorter. They are located at the following places;
Magic Kingdom Park: Guest Services at City Hall
Epcot: Innoventions East or the International Gateway
Disney's Hollywood Studios: Guest Services to your left as you enter the theme park
Disney's Animal Kingdom Theme Park: Guest Services to your left as you enter the theme park
Have a Magical Vacation!