In a 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 in a deep-fryer.
Fry shrimp in bathes: Cook, turning once, for 2-3 minutes, or until golden brown.
Using tongs, remove shrimp to paper towels to drain.
Serve warm with your favorite dipping sauce.