Any time you need a special meal at WDW, you should arrange for it at least 48 hours (preferably more) in advance. Your first step is to call Disney Dining at 407-WDW-DINE and have them make a note on all your table service reservations that there is a vegetarian in your party. If you can, I suggest you call before October 27, as the phone lines will likely be busy for a while after that.
Several of the Moms Panelist are vegetarians or have vegetarian family members. You can read some dining suggestions
HERE,
HERE,
and HERE.
You should also know that there is
an entire department at Disney Dining dedicated to helping guests with
food preferences, allergies, or intolerances, and
religious-based food requirements. Just send an email describing
your situation (at least 14 days in advance of your trip) to
SpecialDiets@DisneyWorld.com.
A cast member will get back to you with the information you need to
make sure that you have a safe, and delicious, visit to WDW.
Another great resource for you is a book called PassPorter's Open Mouse for
WaltDisney World and the Disney Cruise Line. This sells for
approximately $20 and is available through amazon.com and many larger
bookstores. Open Mouse gives incredibly detailed information for Disney
guests with any sort of issue, from anxiety to vegetarianism and
everything in between.
Good luck and have a great trip!