If you're not in the mood to light up the outdoor grill, cook the vegetables in a grill pan.
Preheat grill to medium-high heat.
Remove dough from refrigerator. Let stand at room temperature, covered, for 30 minutes.
Place a pizza stone or heavy baking sheet in oven. Preheat oven to 500° (keep pizza stone or baking sheet in oven as it preheats).
Flatten bell pepper pieces with hand. Arrange all the vegetables in a single layer on a large cutting board or baking sheet; brush both sides with 1 1/2 tablespoons oil. Arrange onion wedges on skewers, if desired. Arrange vegetables on grill rack coated with cooking spray, and grill for 3 minutes on each side or until crisp-tender and grill marks appear. Remove from grill. Coarsely chop bell pepper.
Roll dough into a 14-inch circle on a lightly floured surface, and pierce entire surface liberally with a fork. Carefully remove pizza stone from oven. Sprinkle cornmeal over pizza stone; place dough on pizza stone. Bake at 500° for 5 minutes. Remove the partially baked crust from oven. Spread sauce over crust, leaving a 1/2-inch border. Arrange the vegetables over dough, and sprinkle evenly with salt and crushed red pepper. Top evenly with cheese. Carefully return pizza to pizza stone. Bake at 500° for an additional 12 minutes or until the crust and cheese are browned. Brush edge of dough with remaining 1 1/2 teaspoons olive oil. Cut into 6 large slices.