Birthdate is circa and is based upon quite a bit of research, which has yielded nothing about this daughter of Michael. Daniel Oswalt/d is suspect as a husband too. The only evidence of him comes from Enoch’s history.
The New Bethel church records have a Catharine Hagenbuch appearing as a sponsor for baptisms beginning in 1791. This points to a birthdate for her around 1775 or 1776 (she would have needed to be 15 or 16 to be confirmed and a sponsor). She appears again in 1793. After that, she is gone. She likely turned 18 and got married.
A 1775 birthdate makes more sense given the birthdates of the other children of Michael too.
Enoch states she died in Pickaway County, Ohio. Again, this is suspect, but has been entered.