The card you are asking for is a Guest Assistance Card and more information about Guest Assistance Cards is available in post #6 of the disABILITIES FAQs thread. That thread is near the top of this board or you can follow the link in my signature.
Wheelchairs are allowed in all attractions without a Guest Assistance Card ( there are a few exceptions where guests must be ambulatory that do not allow wheelchairs - one is the Swiss Family Robinson Treehouse in MK and the other is Tomorrowland Transit Authority in MK). If she plans to go to some attractions without the wheelchair and needs to avoid stairs in those lines, she would need a Guest Assistance Card for that, but not to bring a wheelchair in lines. There is a list of 'Mobiity Entrances' from the WDW Guide for Guests with Disabilities in one of be posts in the disABILITIES FAQs thread. If a CM says you need a card to use one of those entrances, ask to speak to their supervisor because the CM is incorrect. It is actually against the law (according to the ADA) to require proof to allow someone with a visible need (like a wheelchair) to use the designated mobility entrance. Guest Assistance Cards are for invisible needs that the CM would hav no way to know about without the card.
You don't need a doctor's note. Again, it is against the ADA for them to require a doctor's note. You can bring one if you want, but chances are that they will not want to look at it. If she has needs that are not met by bringing the wheelchair in line, she may need a Guest Assistsnce Card, but if he biggest need is bring it into lines/attractions, she won't need one.
