Preheat oven to 450°.
Unroll dough onto a baking sheet coated with cooking spray; pat into a 12 x 8-inch rectangle. Bake at 450° for 9 minutes.
Place a large nonstick skillet over medium-high heat until hot; coat with cooking spray. Add onion, and sauté 4 minutes or until golden brown, adding 1 tablespoon water every minute. Add shrimp, remaining water, and balsamic vinegar. Sauté 3 minutes or until shrimp are done and onion is golden.
Coat prepared pizza crust with cooking spray. Spread pesto evenly over top of crust, leaving a 1/2-inch border. Top with onion mixture and cheese. Bake at 450° for 6 minutes or until cheese melts and crust is golden. Cut into 6 squares.