Wrap the beet in aluminum foil and bake until tender, about 1¼ hours. When the beet is cool enough to handle, peel it, and cut it into ½-inch dice.
Cook the potatoes in lightly salted boiling water for 10 minutes. Add the carrots and cook until the vegetables are tender, but not mushy, about 10 minutes more.
Let cool, then cut the vegetables into ½-inch dice.
In a large salad bowl, combine the potatoes, carrots, onion, pickles, peas, beet and dill.
Toss gently, taking care not to crush the vegetables.
In a small bowl, whisk together sugar, vinegar, oil and season with salt and pepper.
Toss the salad with the dressing. Taste and correct the seasoning if necessary.
Cover and refrigerate for 30 minutes before serving, so the vegetables have some time to marinade and absorb some of the dressing.