Hi Barb Re Caroline Baer passenger on the Ceasar Godefroy.
Caroline was the only Baer to travel from Hamburg from 1866 to 1869 She came from Schwiebus in Preussen.
Without knowing relatives it is difficult to see if she was traveling alone.A 13 year old Female traveling alone could possibly indicate an Orphan.
Sorry but I don't know how to locate the passenger lists from the Hamburg end, There are a lot of lists on Findmypast.com.au.
I have a transcribed copy of all passenger lists from Hamburg 1866,1867 and 1869 if you need further look-ups

The Caesar Godeffroy departed Hamburg on 23 May 1868 stopping at Cuxhaven and departing 3days latter, Arriving in Port Adelaide Saturday September 12th 1868.
Graham