In some cases, the doctor can order a saline infusion after a large blood draw, but that wouldn't be done at an outpatient lab, I think. You'd need to be in a hospital lab or the office of a doctor prepared to give saline. They can also do the draws over the course of a several weeks if one is not up to a large one-time draw.
I'm surprised KDM didn't do something to compensate for the large blood draw if your daughter was already weak.