I see several viable options for a fairly responsible 11-year old:
1) Disney Gift Card - you can buy it online or at your local
Disney Store. You can get one now and add a little to it at a time (say, each week or two weeks, that's how I save for my trips), the cards are reloadable, and most important, they are
replacable if lost, stolen, or ruined - all you need is the original purchase reciept. They are good almost everywhere at WDW, including parks, resorts, restaurants and eateries, but there are a few non-Disney venues that can't accept them, so a certain amount of cash is also nessecary.
2) Disney Dollars - fun money good at ANY Disney-owned venue at WDW, also available from your local Disney Store. However, DD$ are not replacable if lost or stolen - they are essentially cash.
3) Room charging - also good at ANY Disney-owned venue that has a card reader. Room charging is done with the room key, which is easily replacable if lost, stolen, or damaged. And you don't have to actually "charge" anything to enable room charging - you can put down a certain amount of cash, travellers checks, or even Disney Dollars at check-in, sorta like a pre-paid credit card. And you can have a list of all the charges printed by the front desk at any time, so you know how much you have left and where it's all gone. If you use it up a little quicker than you thought, you can put more down any time.
My recommendation: Save by getting a Disney Gift Card and adding money to it on a regular basis between now and the trip. Hold onto that original reciept and let aunt and uncle have it before departure, in case the card is lost.
When DD goes to WDW, give her the Gift Card and a certain amount of cash for those places that don't take the card; let her put the gift card down at check-in to enable room charging on her room key, then she will only have to carry the room key and a few bucks in cash around the parks with her. At check-out, aunt and uncle can get a printout of all DDs charges (and refund any left-over money); DD will probably enjoy having the printout as a souvenier ("Oh, I remember when we ate there! I remember what I bought there!" etc).