There is also an 1860 census page for this family. It lists Elizabeth (the daughter) as 6 years old, ie, DOB 1854, and born in "Hessia D", ie, Hesse-Darmstadt. Even knowing that I had to resort to a different search to find her on Family-Search. I have attached the 1860 census to her page on Family-Search. I did not create the other family members. If you think this is the right Elizabeth, you can do that.
The ancestry entry you asked about shows her parents as Johan Valentin Koehler and Elizabetha Katharina Schlitt. Valentin re-married Sophie Schorlemmer 15 Aug 1895 in DeWitt. He appears in 1860,70,80 and 1900 censuses there. His Texas death cert shows death in Meyersville, Dewitt, Texas on 3 April 1906.
If you want full citations, let me know.