Bring 2 cups water to a boil in a small saucepan over high heat. Stir in the quinoa. Cover, reduce the heat to low and cook until the liquid is just absorbed and the quinoa is moist and nearly tender, about 15 minutes.
Transfer the quinoa to a large bowl and immediately stir in the oil, apricots, 1 1/4 teaspoons salt and 3/4 teaspoon pepper. Set aside to cool slightly, about 20 minutes, stirring a couple times. Refrigerate until chilled, at least 2 hours.
When the quinoa is cool and ready to serve, stir in the rocket, basil, lemon juice and pistachios. Add salt and pepper to taste. Sprinkle with the goat cheese and serve.