I am working on my DONA birth doula certification. As far as I know, you have to attend one of their workshops. You cannot bring your baby with you, but you can have someone come by with her like every 3 hours so that she can nurse, and then that someone takes her to watch again, if that makes sense. The reading, test, write-ups, and births are all done on your own, wherever you live.
ETA: I am going with DONA because they are one of the largest, and probably the most well-known, doula organization. With a military spouse, I wanted a "credential", if you will, that was well-recognized. And for people who don't know about doulas and just google search it, DONA is one of the first links that comes up, and they can then search by state and city. That said, I don't like their certification process. But for my situation, I felt that the name was needed.