When it comes to accessibility,
DCL compares pretty well to WDW. As far as the
scooter goes; book yourselfs a handicapped accessible stateroom. You'll need to file out a form with your needs, aids you use and have a doc sign this. Not only will that supply you with the room for the
ECV, but you will find it a heaven sent to have an accessible bathroom for those days you are drained after dialysis. More space to move around, grabbars, sit down shower (depending on type of cat you book and spec. stateroom they even have some staterooms with both a sit down shower and tub!). Also these rooms come with an alarm system, where you can simply push a button and a CM will come and help you out in case of an emergency. This system can be enabled and disabled by guest services on request. Part of that also is a second phone in the bathroom.
To give you an idea; my friend and myself did a 7 night last september in a cat 6 stateroom. She uses a manual wheelchair, I a powerchair to get around outsite of the room and a manual inside of the room. We had them remove the small table to allow more moving space. We had more than plenty space to move around with 2 of us in a chair and one chair 'hanging out', and guests with that. Both of us had a lot of medical supplies with us, combined with all the gift stuff, stuff we bought in the US etc. Don't know about the other cat. staterooms, but the cat. 6 accessible stateroom has a pretty huge -for cruising matters that is- "walk in" closet. We stored 5 suitcases, 3 carry ons next to each other and the stateroom host put the coffee table also in there on it's side.
Common places of the ship tend to be on a good accessible level. You might have to use a different door to get out onto the deck (not all have electric buttons and/or work), and/or have somebody help but that are minor things. Elevators are small, but a regular ECV does fit -tip; practice backing up in a straight line while watching out for folks so desperate to get onto an elevator they seem to want to run you over while getting out

-.
Hallways can be a bit tight, especially when stateroom hosts are doing their work and the carts are out, but they are wide enough to let you pass. As soon as any stateroom host -or any other CM for that matter- see you coming, they'll move their stuff out of the way if need be.
Medical services on board also are

, although that is something I still wouldn't advice anybody to try it out.
Dining, activities; don't worry! They'll work with you. With an ECV you probably wont be able to keep it right at the table in the dining room (size problems), but the CM's are more than happy to work with you, allowing you to drive right upto the table and driving the ECV to a better suitable place and vice versa if you're done and/or need to go to the bathroom. If worried about location of the table; simply go check it out after embarkation. If you find it's not accessible for you, it's easiest to have it changed at that moment, also saving you the flustered and rushed feeling of experiencing that on the first night with the dining room filling up with folks.
A mobility disability and/or being on dialysis aren't a 'no go' for cruising when those same disabilities still allow you to do WDW with aids and/or help. You might want to get yourself a copy of the Open Mouse. It's a book that's all about how WDW and DCL works for those with disabilities. It'll be a great info-source and put a lot of your worries to bed.
Same as with your supplies. When working with DCL, it'll work itself out. You're not the first one, and definately wont be the last. Cruising is a way of travel a lot of folks with a disability love, because this is a way of travel that suits many needs so easily. If you want more info about cruising other than DCL; go and check out
http://boards.cruisecritic.com/forumdisplay.php?f=190 This is a part of the CruiseCritic Board dedicated to cruising with a disability. Lots of info about cruising with lots of cruiselines.
The only real downside to this we've experienced? Having a huge verandah but not being able to reach it independantly caused by the heavy opening system. (even perfectly healthy cruisebuddies found it somewhat of a task opening those slide doors)