My DH and I are vegetarians and would agree with previous posters' suggestions to give Boma or Jiko a try or Crystal Palace. I think Boma was voted the best vegetarian restaurant in central Florida or something along those lines. Re: their soups, they always offers one vegetarian soup, though it's never marked as such so you need to ask one of the chef's to point it out.
Re: the birthday cake, contact whichever restaurant you decide to go to to see what they can do for you. However, if you decide to eat at Boma, they have some really excellent desserts so unless you know that DD's friend would be disappointed unless there was a birthday cake, how about letting her enjoy their amazing desserts? I can't imagine eating at Boma and not having a zebra dome for dessert, but then again, maybe they could provide you with an equally amazing birthday cake?
I haven't eaten at the Brown Derby but have looked at the menu and their vegetarian offering sounds very good! I hope to give it a try on our next trip.