Always a pleasure, this kind of detective work is a lot of fun.
To answer my own earlier question: I just found the marriage record (in Ulm) that is more legible than the birth record, and there it clearly says that her name was "von Prümer".
Here is the most important information from that record:
Name of the groom: Carl Joh[ann] Bap[tist] Damian Junghans
Name of the bride: Clara Maria Antonia v[on] Prümer
Occupation of the groom: assessor in service of the Grand Duchy of Baden
Faith of bride and groom: catholic
Parents of the groom: Georg Franz Junghans, catholic, scribe on Stocksberg Castle & Elisabetha Antonia Mosthaf
Parents of the bride: Udalrich v[on] Prümer, Oberjustizrat in Ulm (deceased) & Maria Anna Mosthaf
Place and date of birth of the groom: Stockheim, November 21, 1797
Place and date of birth of the bride: Ellingen, January 18, 1807
Place and date of the marriage: Ulm, August 3, 1830
It also states that they were related "to the second degree" - both of their mother's maiden names are the same, so that's probably how they were related.