My sons both have egg allergies, and I would give you the exact same answer as deegack above. Disney is fantastic with allergies, Babycakes has egg-free cakes and other treats, and there is a wealth of info on the disABILITIES section of this forum.
There are going to be many egg free choices for your DD, everything from Dole whips to turkey legs to Mickey bars to kaki gori at Epcot. Talk to a chef at TS restaurants about safe choices, and read the allergy binder/talk to a manager at CS. With just the one "top 8" allergy, I think you're going to find it is very easily accommodated and she will have lots of egg-less choices. Good luck!