I would automatically add the mozzarella, as I love cheese, but of course leaving it out makes it suitable for vegans, or even adding a vegan cheese instead (but I think that might a little far fetched for this forum )Sounds good but I think you'll need another name for it. Quesadillos by definition need cheese (queso) Of course if we're talking about lacto-vegetarian you could add the cheese.
~Patrick