To make the cookies: In a large mixing bowl, combine the sugar cookie dough, bubblegum extract, and 1 1/2 cups flour. Divide the dough in half, form into balls, and cover with plastic wrap. Refrigerate for 1 hour.
Remove the dough balls from the refrigerator and unwrap. On a lightly floured board, roll the dough out to 1/2-inch thickness. Cut out bunny-shaped cookies with the cookie cutter.
Place the cookies on an ungreased cookie sheet. Carefully insert the wooden cookie sticks into the cookies, far enough to hold the cookie, but not so far as it comes out the other end. Place the cookie sheet in the refrigerator and chill for 1 hour.
Preheat the oven to 375 degrees F.
Bake the chilled cookies for 15 to 18 minutes, or until golden brown. Remove from the oven and cool on the cookie sheet for 5 minutes. Transfer to cooling racks. Allow cookies to cool completely before decorating.
To decorate: Create the border icing by combining 1/2 pound confectioners¿ sugar with a drop of food coloring, then gradually adding enough water until the mixture is thick but still squeezable. With a piping bag, create a thin border around the perimeter of each cookie. Create the center icing by combining 1 pound confectioners¿ sugar with at least 1/2 cup of water, adding enough to create a thinner consistency. After the border icing has hardened, pipe the center icing onto the middle of the cookie to fill the surface within each cookie. Complete each cookie with a star-shaped dragee for the "eye" and 4 chocolate sprinkles for the "whiskers." Sprinkle generously with sanding sugar.