Debbie,
Thank you for your clear explanation and for sharing the information you found from your contact in Gailsdorf, a town in the district of Schwaibish Hall, in Baden-Wuerttemberg, Germany, where many of the ancestors on my mother's side lived.
The birth document in question does have the O-O symbol. It was hand written just above the child's birthdate in 18.1.1830.
And thank you all for helping to answer my question.