The same evening I killed my first deer(9point) my brother also killed one(7point) mine dropped dead on the spot. My brothers was a different story though. He gut shot it, and we ended up tracking it like you did by following the tracks
without finding any blood for probably 120 yards or so then like a faucet being turned on it just bled like crazy. We continued tracking it with a good blood trail for probably 100 yards, just like it started it all ended and we were back to following tracks. Roughly 25 yards from where we saw the last blood he bedded down and died in a creek on a sand bar with his head in the water. My brother shot him in the intestines and needless to say it wasn't much for eating. That very well could have been your doe if it was gut shot, but by the sound of it's reaction to your shot I would have my doubts that it's your doe.