Having travelled with my DF who needed a wheelchair over time, you do not need a doctor's note to bring a wheelchair onboard. However, the entire ship (Magic) is not completely wheelchair friendly. Parts of it are quite good, but there are a few places to be careful. The cabin doors, except for the handicapped cabins are definately too narrow for a wheelchair. There is a small step from teh cabin floor into the toilet room and the shower room in the cabin. On Deck 9, use the aft elevators because the doors have wheelchair buttons, the forward and midships doors to Deck 9 have lips with ramps, but you need to hold the door for them. Similar problems exist with the doors out to Deck 4. Luminiere's has a side entrance without the steps for handicapped/wheelchair access. My tip is to walk where you think you are going on the ship before heading there with the wheelchair.
The crew is very tuned in to people using wheelchairs - and were fantastic. During lifeboat drill, you will get questions about information they will need in the event of an emergency. The crew was espescially good about helping on the gangway and getting on and off of a tender that was used on that trip.
The other potential issue if cabin space - even folded, a wheelchair takes a big of space. If there are just 2 people in a cabin ( not counting Cat 3 and better) you probably won't trip over it a lot, but if you have more than 2 cabin floor space can be an issue.
Excusions are something to talk to the excursion desk about - you have to be able to get on and off of buses or whatever the mode of transportation is without the wheel chair.
Have a wonderful trip when you go - the wheelchair should NOT be a reason not to go (I know - a double negative)!