In medium bowl, combine egg, 1/2 cup flour, beer and baking powder. Place 1/4 cup flour and coconut in two separate bowls.
Hold shrimp by tail, and dredge in flour, shaking off excess flour. Dip in egg/beer batter; allow excess to drip off. Roll shrimp in coconut, and place on a baking sheet lined with wax paper. Refrigerate for 30 minutes. Meanwhile, heat oil to 350 degrees F (175 degrees C) in a deep-fryer.
Fry shrimp in batches: cook, turning once, for 2 to 3 minutes, or until golden brown. Using tongs, remove shrimp to paper towels to drain. Serve warm with your favorite dipping sauce.