Hi, April! Don't panic! If you have noted on all of your dining reservations that you have special dietary needs, at least you've got the ball rolling! In many cases, they can still work with you, even though you haven't given them 14 days notice.
Before you even finish reading my answer, go right now and email SpecialDiets@DisneyWorld.com. Give them as much information as you can, including your reservation confirmation numbers, your dietary requirements, the names of the restaurants you will be dining in, and the dates and times of your reservations. Note at the top of your email the dates of your trip, so they will know that your vacation is coming up quickly.
You can also call 407-824-5967, which may get their attention a little bit faster. They'll also be able to give you a pretty good idea right away on the phone what can be done.
There are several counter service locations that may also be able to accommodate some of your daughter's dietary needs. You can see the list
HERE.
I hope this helps ensure that your vacation is stress free and wonderful!