In advance: Make cookie pieces. Prepare and roll out dough. Use patterns to cut out head, tail and 2 legs. Use knife to cut 3 supports, each 2 x 2 in. Bake and cool cookies.
Also in advance: Decorate and assemble cookie pieces using royal icing. Use tip 3 to outline and fill-in eyes and nostrils (pat smooth); pipe outline smile. Ice inner ears smooth. Cover head, tail and feet with tip 16 stars. Finish tail end with tip 16 pull-out stars. Let dry. Attach Lollipop Stick to back of tail, leaving 4 in. exposed to insert into cake. Attach support cookies to back of head behind ears and to right of smile. Let all dry overnight.
Bake and cool 1-layer cake. Using buttercream, cover with tip 16 stars. Insert tail. Position head and legs.