The name you found is Kata, but she states she is going to her husband Marko at Etna PA Her next of kin at Turanj (south of Karlovac) was her father Miko GORSIC.I don't believe this Kata is the "Fannie" you are researching as Mark and Kate STAVLENICH are found in the 1930 Etna PA censusand then I find a Soc Sec Death Index for Katharina STAVLENICH in PA
Do you know "Fannie's" maiden name?
You mentioned that "Fannie" and Andrew had a child named Katie.What about the older boys, Frank and John, who was their mother.
Fanny/Fannie is a diminutive of Frances.Croatian Frances could be Franca, Franka, Franja or Francika.
Checking the 1910 census for Sugar Creek MO finds this couple listing Austria as their birthplace.Could this be Andrew and Fannie?