In the small bowl, stir the sweetened flake coconut (not the frozen coconut) with the drops of red food coloring until all of the coconut flakes take on a pink hue. Set aside.
Carve and Assemble
Cut the cakes according to the diagrams below. Use the square as the body of the bunny and the cuts from the square as the ears. Use the small circle as the head of the bunny and the cuts from the circle as the feet.
Bring water to a boil in the pot of the double boiler. Mix together the egg whites, sugar, salt, cream of tartar and water in the bowl. Place the bowl over the boiling water and beat with the and mixer for about 7 minutes, or until the mixture turns white and fluffy and has soft peaks. Stir in the vanilla extract and frost the cake immediately.
Sprinkle the thawed frozen coconut all over the surface of the frosted cake. Add the pink coconut for the inner ears, nose, and the paws. Add cut strings of licorice to the paws, mouth, and eyes. Add jelly beans for the mouth, eyes, and nose. You can add a bow as in the original or some other decoration around the neck.
You can prepare the cakes and coconut a day ahead. The frosting is best used on the day it is made.