I'll break it up so you can decide what is most important based on yours and your friends priorities. I'll touch on quick service dining in the parks but if you need table service suggestions let me know. Any restaraunts you have questions about, I
HIGHLY suggest heading to The DIS'
Disney Dining YouTube page and watching their review. Some are a couple years old but the crew usually gets different items and usually one of them gets a vegetarian or plant based option so that can help your friend find something she'd like.
Magic Kingdom
Classic MK Rides that everyone should experience at least once in my opinion:
-Haunted Mansion
-Pirates of the Caribbean
-Space Mountain (my advice on this is to this at rope drop, the wait fluctuates through the day but it can get pretty bad and it sometimes doesn't go down much until late at night)
-Splash Mountain (maybe not "classic" but wildly popular and leaving soon so your friend should experience it at least once)
-Jungle Cruise
-Carousel of Progress
-Tea Cups
-Peter Pan
-Small World
-Dumbo
-Tiki Room
-Country Bears Jamboree
Thrill Rides at MK:
-Splash Mountain
-Space Mountain
-Big Thunder Mountain
-Seven Dwarfs Mine Train (my advice on this is to do this as your last ride at the end of the night. This ride even with the reduced park capacity and social distancing still easily pushed 1.5-2 hour waits. My family went around Christmas and we would get in line for this around 20 minutes before park close and would wait 30-50 minutes depending on the night)
-The Barnstormer (this one is a kiddie coaster but she may still enjoy)
I realize that I just named nearly every attraction at the park, but MK is so full of historic and great attractions that it's hard to exclude a lot of them. I would try to rope drop and stay in the park as long as you guys can to maximize your chances of seeing everything. Aside from Magic Carpets of Aladdin, there is nothing else I would say is worth skipping on purpose, but the ones mentioned above are ones I feel should be prioritized.
MK QS Dining:
-Peco's Bill is probably the best QS, and it does have some vegetarian options (Southwest salad or you can order one of the rice and bean bowls with no meat) for your friend.
-Your friend won't find anything to eat there, but if you're willing to pick up food from different spots, Sleepy Hollow has a great Spicy Chicken Sandwich and corn dogs.
-Cosmic Rays is not something I'd recommend. It's just burgers and hot dogs and I've gotten cold/non-fresh food from them before
Hollywood Studios
HS Must Do attractions:
-Tower of Terror
-Mickey and Minnie Runaway Railway
-Star Wars Rise of the Resistance
-Toy Story Mania
-Slinky Dog Dash
-Rock 'N Rollercoaster
HS Thrill Rides:
-Tower of Terror
-Rock N Rollercoaster
-Slinky Dog Dash
HS Dining:
-Docking Bay 7 in Galaxy's Edge is definitely somewhere you guys need to go. The Felucian Kefta and Hummus Garden Spread is one of the most popular plant based meals on properties. The rest of the food seems to be pretty well liked as well.
-Ronto's Roasters is another non vegetarian friendly place that is really good that I'd suggest for you. It's basically a sausage/hot dog on a pita but the sauce and slaw makes it really good.
-Woody's Lunch Box is just sandwiches and grilled cheese but is still pretty good, however it closes at 5 so you'd have to do that for lunch/early dinner
-ABC Commisary has a diverse menu and some plant based options so check out their menu this may be a good option for you guys.