Hi Barb I guessed that Caroline was Lutheran from her first name in her home district is usually Lutheran, as Carolyn is Usually RC and Carol Evangelist, this is all deduced from my research.
I find no sign of the Kunoths departing Hamburg 1866-1869 so it is a mystery why she was travelling at 13yrs. Maybe her parents had died and maybe the Lutheran Church sponsored her passage. I'll keep looking every now and again.

Further research proved my guess wrong Caroline Kunoth was buried 10 Apr 1916 in the Catholic cemetery West terrace, Adelaide.