I agree with the previous poster -- it might be tough. So, first, try calling and asking what's still available for a party of three on Thanksgiving and see what they say.
If all is booked, here are some other suggestions:
-If you're renting a car, check out other non-Disney restaurants in the area. There are some good ones and you might be able to reserve something that way.
-If you're staying at a Deluxe Resort, order room service and make your own Thanksgiving that way -- it could be fun for your 10-year-old to maybe pretend that you're like the Pilgrims -- miles from "civilization" and making the most on the available food and being thankful for it. It could be an intimate family Thanksgiving for your family.
-Go to the park of your choice and do counter service, but pretend one of you is a pilgrim, and one is Squanto or Samoset (if I remember their names right -- LOL!), and the Squanto and Samoset can "help the pilgrim" get the food.
The important thing is that you're together as a family. It will be memorable, whatever happens, because of that.
-Dorothy (LadyZolt)