I carry rubber gloves in my pack. The primary reason is so that I don't need to wash my hands in the cold stream after I've cleaned an animal. I think I would have put some on and opened her up. If it is warm enough for flies to be out, it wouldn't surprise me that they were there in a hurry even on a healthy deer.
It is not likely that she was in labor, but if she was she'd be fine to eat.