I may be the odd one out here, but it's my understanding that our bodies are built to naturally detox themselves without having to go on any special diets or fasts so long as you eat clean. If you eat a diet of whole, unprocessed plant-based foods then you're already giving your body everything it needs to keep itself in good functioning order.
Limiting your food variety that drastically especially for that long may have some really negative effects.
If you want to detox, then I suggest staying away from animal proteins, processed foods, caffeine, alcohol, and added sugar. You will not see any long-term negative effects from eliminating these from your diet as they don't do your body any good anyhow.
You will get all the vitamins and nutrients you require to function from a variety of plant-based foods.
The only vitamins you need to supplement are B-12 and D-3.
Minerals: Quinoa has a generous amount of minerals raw according to USDA data. I notice the cooked version, considerably less (throwing cooking water out perhaps?). If you sprout your Quinoa and just lightly steam it, you retain the minerals and most of the vitamin content (as well as added vitamins that appear when sprouting)
Vitamins: I can't see any missing just using these 3 foods except for B-12. As mentioned above, sprouting will increase the vitamin content as well, and introduce some that aren't in Quinoa (like vitamin K) but are in avocados.
If you must boil Quinoa with too much water (which means dumping some of it), I'd suggest Nixtamalization with wood-ash or lime, which will greatly add all the needed minerals in large amounts and some trace ones as well. This actually applies to any grain and other seed type foods like legumes or seeds.