Hi Kim,
I believe you're thinking of the new Be Our Guest restaurant in the Magic Kingdom. Be Our Guest is technically in the Beast's Castle, not Belle's (but I'm sure she ends up there eventually).
Be Our Guest is a bit of an odd restaurant. It functions as a Quick Service venue during lunch (somewhat like a fast food place, but with real plates and much more yum) and as a Table Service venue during dinner (waiters, tablecloths, etc.). The menus are different, but the setting is the same. Another difference is that the Beast is often available to great guests during the dinner hour, but he is not there during lunch.
If you'd like to have lunch at Be Our Guest, you don't need a reservation. I will caution that the line to enter can often be quite long. Lunch usually starts at 10:30am. I've had good luck with eating a very light breakfast and then eating a very early lunch with no wait. If you show up later in the day, you could be standing in the sun for a while.
Reservations can be made for dinner. You can do this via the
DisneyWorld.com website or by calling Disney at 407-WDW-DINE. Reservations may be made up to 180 days in advance. Again, this a popular venue, so the earlier you call the better chance you'll have of securing the reservation you need.
If your granddaughter wants to meet Belle, she can do this during the character dining experiences at Cinderella's Royal Table at the Magic Kingdom or Akershus in Epcot. Reservations are strongly encouraged for these meals.
Belle also greets guests in the Enchanted Tales with Belle attraction at the Magic Kingdom and near the France pavilion at Epcot. Check the free Times Guide as you enter park for details on the timing of these events.
Good luck with your planning. Please let us know what else we can do to help.