RE: gestation for whitetail?
Assuming this was a whitetail, you should not feel bad about taking this doe. That fawn would have been born in winter and would have had a tough time making it in addition to pulling the mother down during the winter.
The only time I have had this happen is when I killed an axis deer. They breed year round, like a cow. If fact, one time I shot a big axis doe in December and while I was gutting her, a small fawn got up and ran off. He was too small to make it on his own, so I really felt bad.