Rinse the quinoa under cold water, then cook it in a saucepan with 2 cups of water according to package directions until tender and the water is absorbed. Fluff with a fork and set aside.
While the quinoa cooks, pat the chickpeas dry with a towel. Toss them in a bowl with the olive oil, oregano, cumin, salt, and pepper. Spread them on a baking sheet and roast at 400°F for 15 to 20 minutes until slightly crisp.
Grate half the cucumber and squeeze out excess moisture. Stir the grated cucumber into the Greek yogurt along with the minced garlic, lemon juice, dill, and a pinch of salt to make the tzatziki. Dice the remaining cucumber half.
Divide the cooked quinoa among four bowls. Top each with roasted chickpeas, diced cucumber, cherry tomatoes, and red onion slices. Spoon tzatziki over the top just before serving.