As someone who has nursed two babies throughout DL - you have so many options. the ladies at Baby Care will become family to you, like they are to us.
Yes - they do have outlets for pumping. There are even two levels of privacy in the Disneyland one (which was original to the park from 1955) - the main breastfeeding area is walled off with rockers and there is a small room inside for extra privacy that is curtained off. There are about 5 rockers in this facility. The 2 Barbaras and Blanche are almost always here.
The DCA area has only 2 rockers, but lots of chairs in the main room. The rockers are curtained off and that facility has a full sized potty for parents (because it is newer and was designed for it). You will usually find Peggy and Angelus here. Linda and Michelle go between the two places.
You can also get additional needs inside - binkies, diapers, food, wipes, you name it. They are there from park opening to closing.
Of course my favorite places to nurse were the Animation Building in DCA, the Aladdin show, Pirates, Small World, any stage show, the Mark Twain Riverboat, and the Railroad. We had friends who had to stop at every opportunity and make a production out of feeding and it made us appreciate the fact that we could feed on the go and not be tied in one location. Some babies aren't that flexible, but ours were.
