Hi Letitia,
How fantastic that you will be celebrating three birthdays during your next visit to Walt Disney World!
Teppan Edo is one of my family's favourite restaurants and is a great choice.
You don't say in your question how many Guests there will be in your party but I can tell you that it does state in the Guest Policies when you make dining reservations at this restaurant that:-
Parties of 8 or more may be seated in different rooms within the restaurant.
Parties of 7 or more may be seated at separate tables.
In my experience 8 Guests are usually seated at each table and there are at least 2 tables situated in each room.
The earlier that you make your dining reservation, the more chance you will have of being seated together so I would highly recommend that you make your reservation at your earliest possible opportunity. Reservations can be made up to 180 days prior to your visit online
HERE or by calling (407) 939-3463.
Wishing you a magical trip!