It's $70.00 to register any dog for any reason online as a service dog. My friend has taken his 200 pound Great Dane "emotional support" service dog with him on 30 + cruises including disney.
There is no such thing as an official service dog registration.
The ADA is specific in that a business cannot require or ask for any documentation or registration of an animal being declared a service animal. (ADA also restricts the type of animal it is meant to cover as a service animal: it is limited to dogs and miniature horses. No cats, rats, snakes, hamsters, pigs or ferrets.)
The only thing a business can do is ask two questions: 1) Is this dog a service dog? and 2) What task is the dog trained to perform?
Emotional support and companion animals do not fall under the ADA definition because they are not trained to perform a task. In the case of these animals, the owner requires only their presence; they don't need the animal to perform a task. Saying "My dog is trained to keep people a certain distance from me" or "My dog is trained to detect differences in body chemistry" or "My dog is trained to assist me in keeping my balance" will qualify your dog as a service dog; saying "Having the dog with me keeps me calm" will not.
Business (like
DCL apparently does) can allow emotional support or companion animals if they want to. Because they aren't covered by ADA they can also request documentation, but as far as I know there is no requirement to pay for such documentation. A doctor's prescription or note is usually OK. Some states have laws that allow the presence of companion or emotional support animals in housing that would not otherwise allow pets, but they don't allow the animal to accompany its owner everywhere (such as into food service areas).
There are outfits online that will send you a "service dog certification" and a vest or special patch or leash, but none of those things are required for a service animal to be designated a service animal. And these items will be sold to anyone who states their animal is a service animal, no proof required. Service animals are not required to wear vests, patches, or have documentation regarding their training or status.
When taking excursions in foreign countries, they're usually done by private companies in those countries which are not bound by ADA. Not sure if a service dog owner will be unilaterally able to take their animal on all foreign shore excursions.
Does Disney have any way of verifying if a dog is truly a service dog and which are simply dogs their owners won't leave behind?
So long as the owner can describe a task the animal is trained to perform, there is nothing the buisiness can do unless the animal becomes disruptive or dangerous. The animal must be permitted to accompany its owner anywhere at the place of business.
There is a case ongoing somewhere regarding a disabled child who brings a service dog to school. The law indicates that while the owner may bring the service dog anywhere with them, the owner also has the responsibility to provide care for the animal. The child is incapable of caring for the animal himself, so the mother is required to accompany him to school in order to make sure his dog gets walked and fed. She is suing the school district in order to force the school to provide one or more school employees to care for her son's service dog. Will be interesting to see how that one comes out.