Check out the disABILITIES FAQs thread near the top of the disABILITIES Board.
There is information about renting at the parks and also about renting from off-site places (including phone numbers and web links for placed DIS posters recommend). As was already mentioned, you don´t need any 'proof' to rent one.
Many people chose to rent one from one of the off-site places because they are smaller and easier to drive, less expensive and you know you will have one for both in the parks and at the resort.
If she hasn´t used one before, it would be good to get some practice in before venturing out in the parks. She should be comfortable going straight, stopping quickly and turning in both directions when going in forward and reverse. She can try them out in stores like grocery stores or Target. If she can drive one of those big ones with shopping carts attached, the WDW ones should be easy.