Put the quinoa and chicken broth in a medium saucepan and bring to a boil. Reduce heat to low, cover and simmer until the liquid is absorbed, 12 to 15 minutes. Fluff with a fork.
While quinoa cooks, heat 1 tablespoon of the oil in a large skillet over medium-high heat. Add the sausage and cook, stirring occasionally, until browned, about 5 minutes. Transfer sausage to a plate.
Add another tablespoon oil to pan, then add the onion and cook until softened, about 3 minutes. Add the squash and carrots and cook about 5 minutes, until the vegetables are tender-firm.
In a large bowl, whisk together the lemon juice, remaining oil, cumin, salt and black pepper. Add quinoa, sausage, squash-carrot and onion mixture and mix. Chill in the refrigerator at least 30 minutes or up to two days. When ready to serve, stir in the parsley.