Hello and thanks for writing. I don't think we have the same woman. The Anna Barbara Fast, mostly documented as just "Ann", who married John Springer in 1819 could not be the one for whom you are looking. John and Barbara were still married in 1834 when their daughter, Keziah/Cassiah Springer was born in Hocking Co., OH. I descend from her.
I do not have Barbara's birth or death date. I haven't worked on this line in a while. For what I have, she is always mentioned as being from PA. This Anna Barbara Fast Springer may have also married John's brother, Jacob Springer. But if you want more Springer and Fast information, I'd go to Hocking Co, since I know they have more Springer info than I have. Hocking Co boarders Fairfield Co. The wills and estates have been helpful.
There were many Springers in the area at that early date, 1800. This seems to be a popular surname. And the German given name of Anna Barbara is very common. I've had several people write to me about women in the area with this name and time period. Good luck. Please let me know if you find any connection.