Set up grill for direct cooking over medium heat. Oil grate when ready to start cooking.
Carefully remove pizza dough from can. Unroll dough and place on hot oiled grill. Let cook 2 minutes and turn over using cookie sheet.
Spread Alfredo sauce over pizza leaving a 1-inch border. Next, top with remaining ingredients in order listed. Cover and cook 8 to 10 minutes, or until cheese has melted and begins to bubble. Serve hot.
INDOOR: Preheat oven to 425 degrees F. Lightly spray baking sheet with cooking spray; set aside. Carefully unroll dough and place on prepared baking sheet. Press out dough with fingers to form 13 by 9-inch rectangle. Bake in preheated oven for 7 minutes, or until crust just begins to brown. Remove crust from oven and top as directed. Return to oven for 8 to 10 minutes, or until crust is golden brown and cheese is melted and begins to bubble.