Hello Steven John and thanks for bringing such an important question to the Disney Parks Moms Panel.
I completely understand your enquiry because although my own youngest daughter isn't a vegetarian, she certainly is a plain eater and doesn't enjoy fussy food at all; therefore I'm happy to share my own families Disney dining experiences with you!
We have discovered that by simply speaking and explaining about our daughters particular food requirements and needs to a helpful Cast Member at whichever
Disney dining location we planned to eat at, we easily overcame any worries or dining dilemmas. Generally speaking there was usually a fuss-free or plain alternative which was suggested to us; including grilled cheese sandwiches & plain pasta dishes! Although of course I can't guarantee that every Disney restaurant will be able to provide a suitable
plain vegetarian alternative for your daughter, my best advice is still to seek the help of a Cast Member at the point of ordering in the restaurant.
I also thought you may find this
Special Dietary Requests link to be an extra useful planning resource.
Have a great Disney day.
~ Jane