I am not a civilian nurse at Walter Redd, but there is information about civilian opportunities here: Welcome to the Walter Reed Army Medical
Check the top right column of the page.
Walter Reed is closing in about 400 days, and services will be split between Naval Hospital Bethesda, and DeWitt at Ft. Belvior which is in the process of building a new hospital.
I've been a patient there, and think it would be an excellent place to work. The staffing was good on the unit I was on (a general post surgical unit). My nurse, the floor supervisor, and the interns and docs were all great. I've also been to several of their clinics, and the staff did not seem overwhelmed. If I lived closer, I would definitely want to work there.