To prepare the dressing, combine the first 8 ingredients in a small bowl; stir mixture with a whisk.
To prepare salad, combine carrot and next 5 ingredients (carrots through chickpeas) in a large bowl. Pour 1/2 cup dressing over carrot mixture, tossing gently to coat. Place 2 cups lettuce on each of 6 plates, and drizzle each serving with about 1 tablespoons dressing. Top each serving with 1 1/3 cups carrot mixture.