A few years back, I got the scare of my life while mowing with my JD LX188. I was mowing the edge of a flowerbed area just next to the woods across the creek from my house, which is like a deer highway. I was mowing right of up the edge of a patch of day lillies when a sudden explosion of brown and white fur erupted less than a foot from my front right tire. It was a tiny fawn who had stayed motionless until I was on top of him. Scared me half to death! Their camoflauge is unparralleled. He scampered into the woods but I'll never forget that.
I too had the same concern, but learned that this is the normal method of care for baby and mama. The Doe forages and returns to feed the Fawn. The fawn stays motionless and concealed unless unavoidable danger ensues. Does should have or soon be dropping fawns, so if you find one like that, leave it be. Mama will return.
If he hadn't flinched I would never have known he was there, as he was in no danger of me running him over.