Preheat the oven to 425°F. Pat the chicken very dry with paper towels, including around the legs, thighs and sides.
Add the carrots, shallots and chickpeas to a deep 9×13-inch baking dish. Toss with 1½ tablespoons olive oil, ¾ teaspoon salt, ¼ teaspoon black pepper, and the reserved chopped rosemary and thyme.
Reserve about ½ teaspoon of the lemon zest for the quinoa. In a small bowl, combine the remaining lemon zest with 1 tablespoon olive oil, 1¼ teaspoons salt and ½ teaspoon black pepper. Rub the mixture all over the chicken and, if easily accessible, underneath the skin over the breasts.
Place one lemon half, the garlic head, and the remaining rosemary and thyme sprigs inside the chicken cavity. Reserve the other lemon half for the quinoa.
Arrange some of the carrots and shallots underneath the center of the chicken to raise it slightly off the bottom of the dish. Place the chicken breast-side up, with the remaining vegetables arranged around it without piling them too high against the sides.
Roast uncovered for 60 to 75 minutes, or until an instant-read thermometer inserted into the thickest part of both the breast and thigh, without touching bone, registers at least 165°F.
While the chicken roasts, combine the quinoa and water or chicken broth in a medium saucepan and cook according to package directions. Remove from the heat and let stand, covered, for 5 to 10 minutes, then fluff with a fork. Stir in the reserved lemon zest and squeeze in juice from the reserved lemon half to taste. Season with salt to taste.
Transfer the chicken to a cutting board and let rest for 15 minutes before carving. Stir the carrots, chickpeas and shallots through the pan juices. If the carrots need a little more time, return the baking dish to the oven while the chicken rests for additional tenderness and light browning.
Spoon about ½ cup cooked lemon quinoa onto each plate and top with the roasted vegetables and any pan juices. Serve the carved chicken alongside or over the top.