I think, the mistery of Dora Hertz, nee Hirsch is solved: She is born 10.11.1861 in Jüchen. The index card of Museum must be wrong. In 1866 is born daughter Bertha to the same parents.
There is no other "Dora" born in Jüchen or Jülich. I add a copy of the birth certificate of Theodora Hirsch, later wife of Jacob Hertz.
Addition