Preheat oven to 350°F. Place 20 paper liners in muffin tins.
In a small bowl, mix the baking powder with the applesauce until it foams. Set aside.
In a large bowl, whisk the flour, sugar, baking soda, cinnamon, and salt together.
Mix in the vanilla, oil, carrots, pineapple, and the applesauce mixture. Mix well until just combined.
Fill lined muffin tins three-quarters full. Bake for 25 minutes.
Remove tins from oven and let cool on a wire rack. Once cupcakes are cool, remove them from the pan. Dust with confectioners sugar by placing the sugar in a small sieve and shaking the sieve gently over the cupcakes.