K.S.
How sweet of you to do this for her! Wow, those are tough allergies, and paired with vegetarian! I'm vegetarian, but have no allergies, so as I was thinking about how I would prepare this I keep thinking 'nope, can't do that.... nope, can't do that!'. Wow.
Anyway, should be easy enough to find the pasta, checking labels to find some without eggs. If conventional pasta seems to all have eggs, check in the gluten free section, they tend to have better versions of things that eliminate one ingredient or another. For the eggplant, I usually peel them (like the taste better) and slice pretty thin. For you, I would dip each piece in rice milk, then dredge in breadcrumbs (again, you may have to make your own breadcrumbs using bread that doesn't have the allergens in it). I bake my eggplant, laying the pieces flat on a pan lightly coated with canola oil, drizzle canola or olive oil on the top and bake covered with tin foil at 375 for about 10 minutes and then remove foil and cook another 5. You could either find storebought sauce that doesn't have offending ingredients, or easily make your own with tomato, garlic, basil, and onion.
Good luck!