Heat oven to 350°F. In large bowl, break up cookie dough. Stir or knead in flour and lemon peel until well blended. Shape dough into 24 (1 1/4-inch) balls. Roll balls in coarse sugar to coat completely. Place 2 inches apart on ungreased cookie sheet.
Bake 10 to 12 minutes or until edges are golden brown. Cool 1 minute; remove from cookie sheet to cooling rack. Cool completely, about 5 minutes.
To make frosting, in large bowl, beat marshmallow creme, butter and vanilla with electric mixer on medium speed until blended. Beat in powdered sugar until fluffy. Place frosting in decorating bag fitted with tip.
Place a dollop of lemon curd in center of each cookie. Pipe frosting around and on top of lemon curd.