Preheat the oven to 350 degrees F. Line twelve 1/2-cup muffin cups with paper muffin liners.
Whisk the flours with the brown sugar, wheat germ, cinnamon, baking powder, baking soda, and salt in a medium bowl. In another medium bowl lightly whisk the egg, then whisk in the vegetable oil, and vanilla extract.
Quickly and lightly fold the wet ingredients into the dry ingredients with a rubber spatula. Stir in the carrots and pineapple just until evenly moist; the batter will be very thick. Divide the batter evenly among the muffin cups. Bake until golden and a toothpick inserted in the centers comes out clean, about 30 minutes. Turn muffins out of the tins and cool on a rack. Serve warm.