By the looks of its snout that is most likely a doe. In Illinois the does drop fawns in early June and I'd have to think its about the same time in S. Carolina or a little earlier but she has plenty of time for the belly to grow.
I take a look anywhere deer bed or have to exert any extra energy, like fence crossing, creeks and ditches. Give those places a short first then check feeding areas and you should come across some.
It is a strange year for deer, there a decent amount of bucks still sporting at least one antler in Illinois. This warm weather has got them all screwed up.