Hey Jane, the profile of Michael Bächtle seems to be a classical conflation to me, at least at first look. The given location of birth clerly is ment to be "Donnstetten" in Württemberg, which is now part of the parish of Römerstein, near Reutlingen in Baden-Württemberg.
There indeed was born a Michael Bächtle, son of Christian Bächtle and Barbara, née Kirsamer in December 1824 (born 6th, baptized 8th) BUT this child died 24th Dec same year, and can not be the Michael in question. This parents are also in many online trees, but are false !!
There is however another hint popping up in Ancestry.com, showing a birth record for a Michael Bächtle, son of Christian and Eva Maria, née Luz. Born 29. Dec 1824 and baptized 31. Dec 1824 in Würzbach, parish of Altburg near Calw, in Württemberg. This would match the date in your profile (at least if you take the baptism).
The fact, that there is a "Frederick Lutz" on the attached passenger list right next to your Michael, traveling together with him, makes it very probable that your Michael Bächtle comes from Würzbach, parish of Altburg !!! It could be a cousin from his mother's side.
Of course the family would have to be researched closely to find a convincing proof.