As a postpartum nurse, I don't have contact with doulas, but I do have lots of interaction with lactation consultants. I would like to reiterate the earlier thoughts that it would be really helpful to have some LC services on night shift. As far as breastfeeding goes, nighttime is definitely the weakest link. You have fewer staff members, fewer helpful partners and the hypnotic blanket of exhaustion in addition to all the regular challenges.
It would be wonderful to have something (someone!) to offer beyond the promise that the LC will see you sometime during the day. We all do the best we can, but I feel terrible when it's a busy night, and I just can't spend a half hour helping a wee one to latch.
I also agree that there are times when supplementation is the right choice. Neither I nor my co-workers appreciate the attitude that formula is somehow just a hair above insecticide for feeding a dry, yellow baby who has lost 10% or more of his birth weight.