Bill Tindall, E.Tn.
While this kitchen item is commonly collected here in E.TN. I have never seen anyone make reproductions. I would think the market for new dough bowls would be thin. I have been told that buckeye was a favored wood. Short of harvesting a tree I don't know where a suitable chunk of buckeye could be obtained.
It would seem that the tools and techniques used to shape and hollow a Windsor chair could be employed. Maybe you can find a local chair maker to teach using the scooping tool and draw knife for the outside.
When you figure it all out post the process and result.