Gradually add sugar to egg in a medium mixing bowl, beating well. Add melted butter, mixing well. Combine oats, baking powder, salt, and nutmeg; add to egg mixture, beating well. Stir in vanilla.
Drop dough by teaspoonfuls 2 inches apart onto lightly greased cookie sheets. Bake at 350° for 6 minutes or until lightly browned. Remove from cookie sheets, and cool on wire racks.