You wouldn't get a baby face. The shape of the face is determined by the bones under it, not by the skin on top. (Although the skin would be smooth, and not lined.) So a face donor recipient does not get the face of the donor.

Also, faces (i.e. skin) is actually the easiest organ to grow, and doesn't need stem cells. I read about a burn victim where they took some skin from under his belt buckle (The only non burned skin on him), and stretched, then split, then stretched some more till they were able to cover him (took months).