If she is 12, it kind of depends on how big of a 12 yr old she is.
If she's over 5 feet tall, she may do fine in an adult size wheelchair, although it may still be wider than she needs. If she's smaller, it would be better to get a smaller wheelchair.
As KPeveler pointed out, there is rental information in the disABILITIES FAQs thread - you will find the thread near the top of this board or you can follow the link in my signature to get there.
If you rent one from home and are traveling by air, you would be able to bring it with you without paying a baggage fee or having it count toward your baggage. You would want to gate check it so it is available until you get onto the plane and as soon as you get off.
DME does have lift equipped buses, or since she can walk, just not distances, she could walk onto the bus and a wheelchair could be loaded underneath the bus with the baggage.
There is more information about both of these things in the disABILITIES FAQs thread (look in post one of that post for the directory).
As KPeveler mentioned, you won't need a note from the doctor to rent one. You may want to look into whether medical insurance may possibly pay for renting one because the need is due to a problem that the doctor says she should limit walking for. Whether or not your insurance would pay varies a lot from policy to policy, the condition the person has and what your deductible and co-pays are. It's worth looking into - if insurance would pay, you would need a doctor's prescription and may need some additional proof, depending on your individual policy.
