Put the quinoa in a medium pot and cover with cold water; let soak 5 minutes. Drain thoroughly through a fine-mesh strainer and put it back in the pot.
Add the broth to the quinoa and bring to a boil over high heat. Reduce the heat to low, cover and cook for 12 minutes. Sprinkle in the edamame in an even layer and add a pinch of salt. Cover and continue to cook, 3 more minutes. Remove from the heat without disturbing the lid, and allow it to rest for 5 minutes. Transfer the quinoa to a large plate and scatter the edamame on top; drizzle with the oil. Spread in an even layer with a wooden spoon, drawing lines in it to cool it quickly.
Transfer the cooled quinoa to a large bowl and add the carrots. Season with 1/4 teaspoon each salt and pepper. Serve warm or chill at least 2 hours, or until ready to serve.