Sailed the Dream early December and had no problems with Vegetarian food (Also ate at Palos and Remy's with no problems). You can go to the
disney cruise line website and under the Disney Dream look at Dining at they have sample menus. Honestly I never felt hungry - had a lot of food - and I think the best thing was trying new foods that I wouldn't have done otherwise.
Some of my favourite food were:
Animators Palate: Black Truffle Pasta Pursuits
(Pasta Purse filled with Truffle scented Cheese and coated with a delicate Champagne Sauce), Creamy Butternut Squash Soup
Enchanted Garden (didn't eat here as we had Remy's) Also didn't have the pirate menu as we were at Palos (I HATE the pirate menu from previous sailings)
Royal Palace: Royal Market Green Salad
(Cherry Tomato, Cucumbers, Peppered Goat Cheese and a Raspberry Vinaigrette) and Pan seared Tofu, (Roasted Zucchini, Eggplant and Red Peppers on Israeli Couscous with a Lime-Cilantro Drop) Tahitian Vanilla Crème Brûlée!!!
Palos - EVERYTHING! The Antipasti selection (aged parmesan, roasted red peppers, Balsamic vinegar), Grilled Portobello Mushroom and Polenta with a Roasted Shallot Sauce and a Parmesan Crisp and of course the chocolate souffle!
Remy's - I had a personalized vegetarian menu (that I have somewhere). Not everything was my personal taste of food but it was an amazing overall experience.
Also I really like the veggie burgers (the same old Disney ones), and always had access to a lot of fruit and other goodies at cabanas and on deck 11. Now I'm super hungry...