Preheat the oven to 350°F. Grease two large baking sheets with oil or butter and set aside.
In a medium bowl, combine the flour, oats, baking soda, coconut, baking powder, cinnamon and salt.
Using a hand mixer or stand mixer in a large bowl, cream together the butter and sugars until light and fluffy. Beat in the eggs one at a time, followed by the vanilla extract.
Gradually add the dry ingredients to the wet ingredients and mix until just combined. Stir in the California raisins and carrots.
Drop tablespoon-sized balls of cookie dough onto prepared baking sheets. Bake for 10-12 minutes, until lightly golden brown. Allow to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
For the frosting, beat together the butter and cream cheese until creamy using an electric mixer in a medium bowl. Gradually add the powdered sugar and mix until fluffy. Add in the vanilla extract and mix until combined.
Spread or pipe the frosting onto the cooled cookies.