Hi, Alan! Service animals are very much welcomed and accommodated at Walt Disney World. There are restrictions with regard to the handling of the animal - such as remaining on a leash and/or harness at all times - and some attractions specifically restrict the use of service animals, due to the nature of the attraction and the safety concerns for all involved. There are also specific areas used as relief areas for the service animals. Click this link to find more information about service animals and the restrictions -
Service Animals at Walt Disney World.
When it comes to Emotional Support Animals, the restrictions are different. Walt Disney World does not permit ESAs. The pet has to be specifically trained to assist in some way with a medical or emotional condition. For example, a service dog for a child with autism may be more of an ESA to the child, but is likely trained to alert the parents of that child if there is potential danger in the child's behavior (trying to leave the hotel unattended or doing something risky like climbing on something dangerous). The same thing with a dog provided to a veteran with PTSD. The dog may be more for the comfort and support of the veteran, but is also specially trained to recognize and alert for erratic or unusual behaviors. ESAs are not afforded the same privileges as a trained service dog under the Americans with Disabilities Act, and unfortunately, they are not allowed in the theme parks or hotels.
You might want to look at bringing the cat with you and boarding her close by, like at Best Friends Pet Care. They are located on Walt Disney World property, and your girlfriend could visit as needed.