Quinoa is a seed, not a grain, so the protein quality is actually quite different that that of, say, oatmeal, in terms of amino acid profile. I blend quick oats and quinoa flakes as a base for muesli, because it provides a better spectrum of aminos than oats alone.
The difficulty of vegan/vegetarian backpacking makes itself quite clear on extended trips, as Ben notes. Your body *will* absorb enough protein, but it will absorb it from your muscles, tendons, ligaments. The same with B12--the body stores some in the liver, but once it depletes that source, you'll become vitamin deficient, and a b12 deficiency can lead to depression, difficulty sleeping, low energy, etc.
As for a handful of nuts providing adequate protein for the day: 1 oz of almonds, eg, contains about 8 g of protein. A moderately active 120 lb person needs roughly 50 g of protein a day, but under physically demanding conditions should probably be aiming for 80-85 grams/day. I love almonds, but that's a lot of almonds (a bag of whole raw almonds from the baking section of the supermarkets is usually 10 or 12 oz and costs 4 or 5 bucks).
Protein intake will vary widely form person to person, according to metabolism, body type, etc, but those are the numbers I use for myself.