Hi Mona and fellow vegetarian! WDW is filled with restaurants of all kinds of flavors and choices that offer vegetarian selections. All table-service restaurants offer a vegetarian entree; and if you don't care for the selection, the chef will often create something different for you!
As for those dining choices that are extra special for vegetarians (and vegans), both Jiko and Boma (My Absolute Favorite!) at the Animal Kingdom Lodge offer plenty of wonderful choices. The California Grill at the Contemporary has a selection called Vegetarian Unplugged, and the chefs have hoot and holler when it is ordered. Within the parks, I've had some yummy meals at the Hollywood Brown Derby (DHS) , Chefs de France (EPC) , the Crystal Palace (MK) , Columbia Harbour House (MK), Cosmic Ray's Starlight Cafe (MK) , Tangierine Cafe (EPC), and Tusker House (AK); all these are included with the dining plan.
You may want to wander over to www.allearsnet.com. Deb Wills has all the menus of the restaurants and a special section devoted to vegetarian dining with an extensive list of restaurants and their vegetarian choices. Happy dining!