Combine flour, baking powder, and salt; stir well. Set aside.
Cream shortening; gradually add sugar, beating until light and fluffy. Add carrots and eggs, beating well. Add dry ingredients, mixing well; stir in coconut.
Drop dough by heaping teaspoonfuls onto lightly greased cookie sheets, 2" apart.
Bake at 400 for 10 minutes or until golden brown. Cool on cookie sheets 1 to 2 minutes; remove to racks, and cool completely.
For frosting, combine all ingredients; beat until light and fluffy. Yield about 1 cup.