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 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.
Ready in 1 hour.