In a rice cooker, or in a sauce pan over a stove, place the quinoa and water. Bring the mixture to a boil and then place a lid on the quinoa and let it simmer for 5-7 minutes, or until the quinoa is tender. Once the quinoa is tender, fluff with a fork and set aside.
While the quinoa is cooking, grill or bake the chicken until cooked through. Season the chicken with salt and pepper. Cut the chicken into bite sized pieces and add to a bowl.
Prepare the vegetables by shredding the carrots, slicing the green onions, dice the red bell pepper, dice the cucumbers and slice the purple cabbage into thin strips. Add all of these vegetables into the bowl with the chicken.
Prepare the dressing by whisking together all of the ingredients together until smooth.
Put the salad together by adding the cooled quinoa to the bowl with all of the other ingredients. Drizzle the dressing over the salad and toss. Garnish with salted peanuts.