Preheat the oven to 475 degrees F (245 degrees C). Spray a baking sheet with cooking spray.
Place sweet potato and Brussels sprouts on the prepared baking sheet. Pour olive oil over top and season with salt and pepper.
Roast in the preheated oven until tender and lightly browned, 15 to 20 minutes, checking every 5 minutes to make sure veggies aren't overcooking. Remove from the oven and let cool, 15 to 20 minutes.
While veggies are cooling, place quinoa in a mixing bowl and stir in beets and cranberries.
Combine vinegar, sugar, onion, poppy seeds, salt, and dry mustard in a bowl for dressing.
Stir cooled vegetables into quinoa mixture. Add dressing and feta cheese and mix gently. Can be served at room temperature or cold.