I have no idea whether Disney cards do this, but you can get her a credit card. I don't know whether she can do it without a co-signer.
We wanted our oldest to head off to college next fall with an understanding of how to manage a checkbook and a credit card . . . so I helped her obtain these items at our credit union last summer. Right now, as a high school senior, she's using them with my supervision, and she's doing well: She doesn't write many checks, but she knows how to do it. She uses her ATM card more often. She practices reconciling the statements each month, and she pays the bill with online banking. She'll go away to college knowing the basics. I feel good about that; as we've talked about college I've realized that my oldest is very, very nervous about her ability to handle money well -- she wants advice, she wants to learn how to manage her finances.
She's had a savings account at the credit union for years. The accounts she opened last summer are "minor accounts" with my name on them; when she turns 18 this summer, we'll change that. I asked that she be given a credit card with a $300 limit -- they wanted to give her more. I see that as enough to fix a tire or a small emergency, but not enough to get herself into trouble.