1. Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
2. In a mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.
3. Add the egg, key lime juice, and key lime zest to the mixture and mix until well combined.
4. In another bowl, whisk together the gluten-free flour, shredded coconut, baking powder, and salt.
5. Gradually add the dry ingredients to the wet ingredients, mixing until a dough forms.
6. Chill the dough in the refrigerator for about 30 minutes.
7. Once chilled, scoop tablespoon-sized portions of dough and roll them into balls.
8. Roll each ball in powdered sugar until fully coated.
9. Place the dough balls on the prepared baking sheet, spacing them about 2 inches apart.
10. Bake for 10-12 minutes or until the edges are lightly golden.
11. Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.

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