Why not put a "bento box" style breakfast together the night before? Add some sort of meat (Protein), veggies and/or fruit (Carbs), and some nuts or slices of avocado (Health Fat). Voila! A healthy breakfast on the go.
P.S. Nut butters/nuts can be both a source of protein and fat. Eggs are a protein source, not dairy.
Be creative, and put in things you enjoy.