I would do some research as there are some places around Disney that I think you could do something very simple without spending a fortune. I've read about Leu Gardens and the Royal Chapel that may offer something just like you are looking for. So although you would not be married in Disney, you would be close, you could make it part of your Disney vacation, and then you could celebrate in your favorite place (Disney
).
Not knowing the specifics of the license, I would keep in mind that you may not be able to keep it a complete surprise from your fiance as she probably will need to sign something to obtain the license before you get married.
Ooh - this leads me to an idea...what if you surprise her with a limo or town car & driver, head to the clerk's office or wherever the license is obained, and just do the ceremony there? You could tell her you have something special/fancy planned and that she should dress nice or if it fit in your budget, you could set her up with a spa treatment or a beauty treatment first.. And then you could celebrate at a nice dinner at Disney...
If you do your homework, I'm sure you could pull off something very magical...