Heat the olive oil in a large pot over medium-high heat. Add the onion, celery, carrots and Cajun seasoning and cook, stirring occasionally, until the vegetables are slightly soft, about 4 minutes.
Stir in the quinoa, then add the chicken broth, 3 cups water, 1/2 teaspoon salt, and pepper to taste. Partially cover and bring to a simmer, then reduce the heat to medium and cook until the quinoa starts to soften, about 12 minutes. Add the broccoli and cook, uncovered, until just tender, about 5 minutes. Add the chicken and stir to warm through. Season with salt and pepper.
Ladle the soup into bowls. Top with the sour cream and Cajun seasoning to taste.