Heat oven to 375° F. Cook the quinoa according to the package directions.
Meanwhile, toss together the carrots, onion, 2 tablespoons of the oil, ½ teaspoon salt, and ¼ teaspoon pepper on a rimmed baking sheet.
Roast, tossing once, until the carrots are beginning to soften, 13 to 15 minutes.
Brush the fish with the remaining 2 tablespoons of oil. Season with the paprika and ¼ teaspoon each salt and pepper.
Nestle the fish in the carrots and roast until the fish is opaque throughout and the vegetables are tender, 10 to 12 minutes more.
Place the fish and vegetables over the quinoa and sprinkle with the parsley. Serve with the lemon wedges.