As long as she is safe and warm, ignore the whining. Close your doors so you don't hear her as well. Does she have food, water, pee pad, bed, crate, etc in her fenced in area? Small crates to sleep in make pups feel more secure. Give her a treat when you put her in there.
You are right, she is very young, and she has chosen you as her pack mate and does not want to be separated from you at all, even at night. If you have an old tee shirt of yours you can wear and then give her in her fenced in area, that might help. Other people use stuffed animals with ticking hearts in them.
If you give in to the whining and get up to comfort her, you are teaching her that whining is rewarded.
Good luck!
