To prepare dressing, combine first 7 ingredients in a small bowl, and stir well with a whisk.
To prepare salad, cook tortellini in boiling water for 6 minutes. Add shrimp and carrot; cook 3 minutes. Drain well. Combine pasta mixture, tomato, peas, and onion in a large bowl; pour dressing over salad, tossing gently to coat. Cover and chill 30 minutes.