1. To make frosting: Add all frosting ingredients to a mixing bowl; beat until light and fluffy.
2. To make cookies: Add the flour, baking powder, and salt to a mixing bowl; stir to combine; set aside.
3. Add shortening to a large mixing bowl; cream.
4. Gradually add in sugar, beating until light and fluffy.
5. Add in the carrots and eggs; beat well.
6. Add in dry ingredients; stir to mix well.
7. Add in coconut; stir to mix.
8. Drop dough by heaping teaspoonfuls onto a lightly greased baking sheet; place 2-inches apart.
9. Bake at 400 degrees for 8-10 minutes or until golden brown.
10. Let cool on cookie sheets for 1-2 minutes, then transfer to rack and let cool completely.
11. Frost with Orange Frosting.