A number of additional children - perhaps checking their birth/baptismal records in the various locations listed for their births would clarify the parentage.
Is there any evidence that her parents ever married?
Julianes parents were married Aug 14 1859 in Vang, Hedmark, see #18. The father Johannes Johnsen was 37 years old and the mother Olia Larsdatter was 29 years old.
You didn't care for the census of the mother and daughter that I already posted?
That census gave a birthplace for the mother and with the other material given above you can approximate her birthyear. Have you started to check those parish records?