1. To prepare dressing, combine first 10 ingredients in a medium bowl, stirring with a whisk. Gradually add oil, stirring constantly with a whisk. Set aside.
2. To prepare salad, place quinoa in a fine sieve, and place sieve in a large bowl. Cover quinoa with water. Using your hands, rub grains together for 30 seconds; rinse and drain. Repeat procedure twice. Drain well.
3. Combine 1 3/4 cups water, quinoa, and 1/4 teaspoon salt in a medium saucepan; bring to a boil. Cover, reduce heat, and simmer for 10 minutes or until liquid is absorbed. Remove from heat; fluff with a fork. Combine quinoa, remaining 1/4 teaspoon salt, blood orange sections, avocado, and kumquats in a large bowl, tossing gently to combine. Add dressing; toss gently to coat salad. Spoon 1 cup salad onto each of 4 plates; top each serving with about 1/2 cup beets.