you don't want to put in a whole egg, the whites aren't digestable raw. If you put an egg in, just put in the yolk. And the texture won't be weird. It will be nice and thick and possibly a little more creamy, but it won't be a gross egg texture.
whole milk or whole milk yogurt and peanut butter in smoothies sound like great ideas. will she drink "milkshakes"? (frozen strawberries/peanut butter blended with yogurt and milk and maybe an egg yolk for a thick milk drink? If she wants it sweeter, since breastmilk is sweeter than cow's milk IIRC, add a little honey or maple syrup)
I don't think focusing purely on calories is ever a good idea (except maybe for like a week long period in a disaster zone, but really, never). Focusing on protein and healthy fat and nutrient rich foods and drinks makes much more sense, otherwise you end up with empty calories.
How about barely sweetened homemade eggnog? I know it might not be seasonal, but hey. It's cream, milk, and eggs, with a little maple syrup. the eggs make it thicker. very calorie rich, and also full of protein and healthy fats and nutrients.