Combine yeast and 1/4 cup warm water in a 1-cup liquid measuring cup; add sugar, and let stand 5 minutes. Add oil.
Position knife blade in food processor bowl; add yeast mixture, flours, and salt. Process 30 seconds, stopping once to scrape down sides. Pour 3/4 cup lukewarm water through food chute with processor running; process until blended and dough is soft.
Turn dough out onto a work surface, and knead until smooth (about 2 minutes). Place in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in bulk.
Punch dough down. Sprinkle 1 tablespoon all-purpose flour over work surface. Turn dough out onto floured surface, and knead lightly 4 to 5 times; roll into a 15- x 10-inch rectangle. Place dough into a 15- x 10- x 1-inch jellyroll pan coated with cooking spray.
Cover and let rise in a warm place, free from drafts, 30 minutes or until doubled in bulk. Spray dough with cooking spray. Bake at 450° for 10 minutes; set aside.
Coat a large nonstick skillet with cooking spray; place over medium-high heat until hot. Add chicken, fennel seeds, and salt; cook, stirring constantly, until chicken is no longer pink. Drain. Sprinkle tomato evenly over crust, leaving a 1/2-inch border. Spread chicken mixture evenly over tomato. Arrange mushrooms over chicken mixture; sprinkle remaining ingredients evenly over pizza. Bake at 450° Broil 5 1/2 inches from heat (with electric oven door partially opened) 6 minutes on each side or until done.