hi Steve, I'm a vegetarian, and I agree with all the others. I've heard of fully-developed adult dogs living a vegetarian --lacto-ova -- life, but I really don't know how healthy that is for the long term. Your pup isn't even fully developed yet. Even once she reaches her full size (about 18-24 mos), I certainly don't see how you can pull this off without giving eggs, which are a rich source of protein and other nutrients.
Dogs can be lactose intolerant, especially in the massive doses of dairy products that you would need to feed to provide the protein and enzymes that your dog isn't getting from any other animal sources.
I feed my dogs a home-made diet. I feed them a large variety of vegetables. But I do feed them meat. I just can't see a way around it.
Here's what it boils down to for me. We vegetarians are usually vegetarians because we have some strong principles or ethics that require us to abstain from meat. But those same strong ethics should require us to give our dogs the best nutrition possible. If we are unwilling to do so, then we really need to re-think our decision to have a pet that is omnivorous and needs a heavily protein-based diet.
I have chosen to purchase mostly organic and grass-fed meat and organic poultry, from local farms as well as certain species of wild fish. I buy it at my health food store. It's not perfect. But many of my reasons for abstaining from meat myself are mitigated -- including horrific treatment of the animal by industrial farming; no hormones, antibiotics, etc; a smaller carbon and pollutant footprint on the environment, etc.
Ultimately, I can't treat my dogs improperly because I have ethics that dictate that I, myself, don't eat meat. That's contradictory in so many ways to me.
BTW, GSDs fed a single food for a long period of time *tend to* develop allergies to that food. So even if feeding soy-based proteins like tofu every day were practical (I don't think it is), you may just end up with a dog that is allergic to soy.
Sorry there isn't better news. Being a vegetarian is rarely convenient, is it?