Preheat oven to 350°F Line twelve 1/3-cup muffin cups with paper liners. Sift first 5 ingredients into medium bowl. Using electric mixer, beat sugar, oil and eggs in large bowl until well blended. Add dry ingredients to egg mixture in 2 additions, beating until well blended after each addition. Mix in carrots and pineapple. Spoon batter into prepared muffin cups, filling each 3/4 full.
Bake cupcakes until tester inserted into center comes out clean, about 30 minutes. Turn cupcakes out onto racks and cool completely. (Can be made 1 day ahead. Cover; store at room temperature.)
Spread top of each cupcake with scant 3 tablespoons Ginger-Cream Cheese Icing.
To make the icing: Using electric mixer, beat cream cheese and butter in large bowl until smooth. Add powdered sugar and ginger; beat until fluffy and smooth. (Can be made 1 day ahead. Cover; chill. Bring to room temperature, then beat until fluffy before using.).