In a sieve rinse quinoa under cold running water until water runs clear.
In a small saucepan bring water to a boil with quinoa and salt and simmer mixture, covered, over moderately low heat until just cooked through, 5 to 10 minutes. Drain quinoa in sieve (do not rinse) and spread out on a plate to cool.
Peel turnip and cut into 1/3-inch cubes. Mince garlic. Slice scallions thin on the diagonal and cut beans into 1/3-inch pieces.
In a steamer set over 1 inch boiling water combine squash, turnip, and garlic and steam vegetables, covered, 7 minutes, or until almost tender. Add beans, quinoa, and salt and pepper to taste and steam 3 minutes, or until beans are crisp-tender. Transfer mixture to a bowl and toss with scallions.