Hi! We are DVC members and travel there often. I am vegetarian but my DH is not. I never call ahead or note it on the reservation. It is really not needed.
At O'Hana's any chef can make the vegetarian option just tell them at the podium and your server that you'd like to request that. HOWEVER, if Chef TJ is working you will have an adventure. He was the Chef at Boma's at one time. He provides vegetarian meals WAY above and beyond the "usual" vegetarian option. He typically works Monday-Saturday. However, he was off on our last trip during these days. (He gave us this schedule on one of our recent trips.) So, I'd ask at check-in if he is working. Even if you get the "usual" it is good! I like the salad they offer as an appitizer as well as the Hawaiian bread. If you book your meal an hour and a half or so before fireworks you can go out on the beach and watch the fireworks and the water parade.
Le Cellier allowed me to out together a meal using just sides on our last trip and it was one of my best meals on that trip. (They do offer a vegetarian option but I have had it many times and wanted something new.)
Nine Dragons had a wonderful meal I enjoyed recently.
Sanaa is wonderful and if possible come for a noon reservation to watch the opening ceremony and you might can score a savanna view table.
The Wave at the Contemporary is awesome! A must try!
Kouzzina is at the Boardwalk and is a new twist with Greek dishes.
Outside Disney I DO NOT eat at a buffet. However, two in WDW are GREAT for vegetarians. I highly recommend Boma (Animal Kingdom Lodge) and Crystal Palace (Magic Kingdom).
For Counter Service you will want to try Sunshine Seasons in the Land at EPCOT, Wolf Gang Puck Express in DTD, and Earl of Sandwich in DTD. I also love the Tangierine Cafe' in EPCOT.