As others have stated, you can use your debit card at WDW, but I think it's better to use a credit card when traveling. Much less liability if lost or stolen.
ETA: Something to be aware of is that many hotels will place a "hold" the entire amount of your stay on a debit card, right from the beginning of your trip. They're even allowed to hold an amount that they "estimate" your charges to be -- which can often be higher than the amount you'll ultimately be paying when you check out. Lots of folks are not aware of this, and it could cause you to overdraw your account because that money is behing held from the day you check in. If they're "holding" $2,000 or $2,500 on your checking account at the resort from the moment you check in, you could be in big trouble.
I was at a Doubletree hotel a couple of weeks ago, and they even had a sign posted at their front desk that if you use your debit card to pay, you should be aware of what might happen if they put a "hold" on your account -- and that sometimes it takes several days after you check out for that hold to be released! This even happens at gas stations - you might only be buying $40 worth of gas, but they might "hold" $100 or more until the debit clears a couple of days later. I work for a credit union, and our members have told us that some merchants (especially gas stations) do this on a regular basis - the customers find they've overdrawn their accounts without even knowing it!
Don't know WDW's practice on this, but it's definitely something to be aware of. Just remember, debit cards work very differently from credit cards!