Place the Froot Loops on a flat surface and cover with waxed paper or plastic wrap. Using a rolling pin, crush to fine crumbs. Do not mix the crumbs, as you want them to transfer variegated color to the cookies.
Combine the flour, baking powder, and salt in a medium bowl. Set aside.
Place the butter in the bowl of a standing electric mixer and beat until light. Add the sugar and vanilla and beat until light and fluffy. Beat in the reserved flour mixture.
Working with a piece at a time, shape the dough into balls about 1 inch in diameter. Carefully roll each ball into the crushed Froot Loops.
Place the coated cookies on an ungreated cookie sheet.
Bake in the preheated oven for about 14 minutes or until golden.
Remove from oven and transfer immediately to cooling racks.