It looks like what you have here is a false pregnancy. The most major sign of a false pregnancy is when a doe pulls fur so early, usually around 18 days past breeding, or not breeding. That fits with the time frame. for her to pull fur 10 days early is too early to think that she is actually pregnant. Even so, it is possible I guess. If you want to leave the nest there until her due date it won't hurt, just in case she is actually pregnant.
As for special care instructions, if she is pregnant,she will probably want more food from now on, and after she has her babies increased food and water is very important to keep good milk production. As for caring for the babies, she should do that on her own. Don't worry if you don't see her feeding the babies all the time. They aren't like human babies who need to be fed every two hours. Momma bunnies will usually only feed their babies once per day in the frst wek of their life, and as they start to open their eyes at 10 days and explore, they go up to momma and drink for themselves.
And as for taking the babies out of the nest, that will be between you and her. If she defends her nest from you, you most likely don't need to worry about how the babies are doing and you will see them when they start to explore out of their nest. If she does let you take the babies out, just make sure that their tummies look full.
and a proper nestbox would be best as everyone else suggested.
Good luck with your doe and keep us updated!