In a medium lidded saucepan, combine the quinoa and water and bring to a boil. Cover, turn the heat to low and simmer for 15 minutes, until the quinoa is al dente. Uncover and remove from the heat.
Meanwhile, heat 2 tablespoons oil in a large wok or nonstick skillet. Saute the carrots, shallot, and white scallions over high heat until soft and beginning to brown, about 6 minutes. Season with salt. Add the garlic, ginger, and green scallions and stir fry until fragrant, another 2 minutes. Fold in the quinoa and stir fry until well-coated in the vegetable mixture and beginning to toast, 3 minutes. Stir in the soy sauce, sesame oil, and sriracha.
Push the quinoa to the side of the pan to create a well. Pour the eggs into the well and cook, stirring gently, until nearly set. Toss the fried rice with the eggs. Transfer the quinoa to bowls and serve right away.