Heat oil in a saucepan over medium-high heat. Cook onion in oil for 5 minutes, or until translucent. Add carrot, and cook 3 minutes more. Stir in quinoa and vegetable broth, and bring to a boil. Reduce to a simmer, cover, and cook 15 to 20 minutes, or until quinoa is tender and fluffy.
In a bowl, toss quinoa together with walnuts and parsley. Serve hot or at room temperature.