I have a Mary Doud in my tree, born in 1849 to Roger and Rebecka Doud. She may not be your Mary Doud--she was born presumably in Mercer, Illinois, and died in 1860.
However, her family did live in Powesheik County by 1870. Her parents had another daughter named Mary (who also went by Margaret) born in Mercer in 1860; she lived to adulthood but never married.
Roger's brother Peter lived the next farm over (both in Mercer, IL, and in Powesheik Co, IA). He had only one daughter I know of (Elizabeth, b.1850).