Heat gas or charcoal grill to medium heat. In large bowl, combine bell peppers, onion, mushrooms, zucchini and vinaigrette; toss to coat.
Place vegetables in grill basket. Place basket on gas grill over medium-high heat or on charcoal grill 4 to 6 inches from medium-high coals. Cook 8 to 12 minutes or until tender, stirring once or twice.
Meanwhile, cut 14 x 14-inch piece of heavy duty foil; spray foil with cooking spray. Place dough on foil; starting at center pres dough to 12-inch round. Place dough on grill ( after vegetables are grilled), foil side down. Cook, uncovered, 3 minutes or until bottom of crust is light golden brown. Remove from grill.
Using wide spatula, flip crust over so uncooked side is down. Spread gourmet cheese spread evenly over crust; top with grilled vegetables. Sprinkle with mozzarella cheese and tomatoes.
Place pizza onto grill, foil side down. Cook, covered, an additional 3 to 4 minutes or until crust is golden brown and cheese begins to melt.