People have posting about doing Disney on dialysis in the past.
In general, you would work with your current dialysis center to get everything set up. Most dialysis centers have helped patients go on vacation, so will be familiar with what to do.
The staff at your child's current site usually would take care of getting doctors orders, insurance coverage and scheduling.
Here are some helpful links that I copied for you from post 3 of the disABILITIES FAQs thread. It is located near the top of this board or you can follow the link in my signature.
Dialysis
Travel Tips from the Kidney Organization.
Aug 2011 thread about dialysis with lots of good information
Thread about dialysis with links to other threads about dialysis.
Aug 2009 thread with some dialysis experiences.
You will also want to look into using a stroller (if its a small child)
Special needs stroller (for an older child)
Or wheelchair (for older child or teen).
There is information in post 2 of the disABILITIES FAQs thread about
renting strollers, special needs strollers and wheelchairs.
All attractions are wheelchair accessible to the point of boarding except Tomorrowland Transit Authority, Swiss Family Robinson Treehouse and Tom Sawyer's Island. You would be able to bring a wheelchair into any attraction/ line with nothing but the wheelchair.
If using a stroller or special needs stroller, the CMs may not recognize those as mobility devices. So, for those, you would need to get a sticker and Guest Assistance Card (GAC) identifying it as a stroller being used as a wheelchair.
You can find out more information about this and about GACs in general, in post 6 of the FAQs thread.