1. Preheat oven to 350°F. Line 2 large baking sheets with parchment paper.
2. Knead dough and flour together until smooth. Roll out to 1/4-inch thickness. Cut out bunny shapes using a 3-inch cookie cutter. Transfer to baking sheets, spacing 2 inches apart. Reroll scraps; continue cutting to get 24 bunnies.
3. Bake cookies, rotating sheets halfway through, until golden, 10 to 12 minutes. Transfer to a wire rack to cool. Make cookie frosting: Stir confectioners' sugar, egg-white powder and 3 Tbsp. warm water until smooth. (If frosting is too thick, stir in more water, 1 tsp. at a time.) Spoon 2 Tbsp. frosting into a ziplock bag. Tint remaining frosting light pink with a drop of red food coloring. Keep frosting covered to prevent drying.
4. Working on 1 cookie at a time, spread a thin layer of pink frosting on top. Sprinkle top of frosted cookie with light or dark pink decorating sugar to coat, shaking off excess. Snip a small corner from bag with white frosting. Pipe a few dots of white frosting on cookie; attach décors. Repeat with remaining cookies. Allow cookies to dry, 1 hour.
5. Place chopped coconut in a ziplock bag. Add a few drops of green food coloring; massage to tint coconut evenly. Put coconut in a shallow bowl. Spread vanilla frosting on cupcakes. Roll edges in green coconut. Press a cookie on top of each cupcake.