Since someone else mentioned already that there are break areas for dogs, I'll just address the anxiety issue.
My dog is not a service dog of any description. I will never take her anywhere dogs aren't allowed (and Disney is right out!). But I have brought her to crowded events and street festivals where dogs are allowed.
Every dog is different, and one would hope a responsible owner would not put their dog in a situation that would make it anxious. Or where it might behave badly.
In my dog's case, when it gets very loud and crowded, she simply sticks close to my ankles and pants a bit. If I'm standing still, she'll position herself between my feet. If I think there's a danger of her getting stepped on, I will pick her up. But she's about 20lbs, so I prefer not to have to carry her unless it's absolutely necessary. She does not bark, and she does not "make messes", except when directed to do so on grass or snow.
She's generally very friendly with people who speak to her, licking them and rubbing her body on their ankles. She ignores people who ignore her. In the rare event someone is trying to pet her and she's not interested, she'll look away and turn her back on them. She's never, in her entire life, snapped at a person. Not even when provoked. I once saw a toddler pull her ear, hurting her, and my dog gave a high pitched yelp, then turned and licked the child's hand (yes, the parent and I were both watching closely - the child was simply fast and unpredictable).
All of which is to say, IF my dog was an Emotional Support Dog, and IF I brought her to Disney World, I'm sure she would have no difficulty with the crowds and I expect she would behave just as well she always does.
Your dog sounds like a wonderful pet. I have no doubt that your dog's excellent temperament and training would make her a likely candidate for an Emotional Support Dog or even possibly a Service Dog. I would not worry about her behavior at WDW.