I would say the doe will likely be just fine. Deer have simply amazing immune systems and recuperative powers. A friend of mine shot a 4 pointer a few years ago that was running around just fine. When he skinned it out he found an entire arrow lying in the body cavity along his spine. Everything was all healed over and that buck had likely lived with that arrow for at least a year. Someone must have shot it from the front through the chest and miraculously missed all the vitals.