The photo was taken by M. E. Muench photographer, located at 1472 Third Ave, in New York City.
Handwritten on the back is the identification of this sweet little girl as Sophie Bielenberg Dettmar, with the notation that it was taken on April 30, 1876.
I have found a possible match in the marriage records of Manhattan with the marriage on July 18, 1897, between Sophie Bielenberg and Adolp J. Dittmer. I've not been able to find them in the census records for 1900. (There is a Sophie Dittmer, aged 32, living in Manhattan as a dressmaker and shown as single. Maybe Adolp died shortly after the marriage?)