Check out:
http://www.wdwinfo.com/Just_for_kids/childcare.htm
The short answer is yes, Disney has child care centers at the Deluxe hotels, children must be potty trained and 4 years old. Cost is $11 per hour, meal included. For children younger than that, there are several non-Disney companies to choose from that provide in room babysitting.
FWIW, my kids stayed at the Cubs Den at WL years ago and loved it. They were disappointed when we came & picked them up