Heat oven to 350°F.
Beat together butter, sugar and egg in large bowl until fluffy. Stir in flour, salt and baking powder. Divide dough in half; cover with plastic wrap and refrigerate at least 1 hour.
On lightly floured work surface, roll half of dough out to 3/16-inch thickness. Use Easter egg template to trace eggs onto dough; cut out with sharp paring knife. Place on ungreased baking sheets. Repeat with other half of dough. Or for bunny cookies, roll half of dough out to 1/8-inch thickness. With 2-1/2-inch bunny or other animal cookie cutters, cut out animal shapes. Place on ungreased baking sheets.
In 350°F oven, bake egg cookies until lightly golden, about 10 minutes, or bake bunny cookies for 7 to 8 minutes. Cool cookies on baking sheet placed on wire rack.
Divide Decorator Icing in half. To one-half, add water, drop by drop, to make good spreading consistency. Divide among small bowls; tint with food paste colors. Spread icing evenly over cookies; let dry.
Divide remaining thicker icing among small cups. Tint with food paste colors. Spoon into pastry bags, one fitted with medium-size writing tip and another with medium-size star tip. For carrots, use bag with writing tip, squeezing bag very firmly, to make thick carrot.