If you're going to do it, I think you should firstly get really clear as to WHY you're doing it.
Meaning, why VEGGIE? Is it for HEALTH reasons, or ANIMAL WELFARE reasons? Will you sacrifice health to make a bit more profit?
I'm not saying you would, I'm just saying that you should get really clear on what you want to create so that you have a better chance of creating it. If for example your mission/intention/goal is "To bring healthy vegetarian choices to the fast food market." you might not even do it by opening up a fast food chain. Maybe, instead, you find yourself working at an already established fast food joint in charge of all their vegetarian choices dishes, where you work with them to bring vegetarian dishes that are healthy to the public at prices they can afford and at the same time the company makes $$$.
If your intention is to open a restaurant, that's different then bringing veggie dishes to the public.
This sounds like an awesome idea and if you're passionate about it, go for it! I'll eat there!
Just take some time to get clear on what is it actually that you want to accomplish. What's the end result. THEN look at how you'll do it, not the other way around.
Just my 2 cents.
Personally I think it's an awesome idea. THere's no reason why fast food + healthy food can't be brought together.
All the time at work at lunch I hear people saying "Where can we go that's fast, healthy and cheap?" and everyone's always saying "Nowhere".
If someone actually makes that happen, my guess is that they would become billionaires very quickly. Even taking "cheap" out of the equation and replacing it with "affordable" would still be a winning formula.