Stir white sugar, vegetable oil, and eggs together in a large mixing bowl until thoroughly combined.
Whisk flour, baking powder, baking soda, cinnamon, and salt in a separate bowl.
Stir flour mixture into liquid ingredients until thoroughly moistened. Mix in carrot, pineapple, and 1 teaspoon vanilla extract.
Pour batter into the prepared muffin cups, filling them to the top.
Bake cupcakes in the preheated oven until a toothpick inserted into the middle of a cupcake comes out clean, about 20 minutes. Set aside to cool completely.
Cream butter with cream cheese with an electric hand mixer in a bowl until smooth.
Beat in confectioners' sugar, vanilla extract, and milk to make a spreadable frosting; frost the cooled cupcakes.