I have just read your post from 2013. I am also researching Peter Petersen, son of Peter Sorsen and Caroline Petersen, who is also my 2nd great grandfather. His daughter, Mary Christina Petersen (Steley) was my great grandmother.
I have Peter Petersen travelling to Australia aboard the Reichstag, departing Hamburg on 13 June 1876, arriving on 6 October (age 23). Also travelling on the Reichstag, as free passengers, were Carl Petersen (age 20) and Jens Petersen (age 19). It is possible that these three were brothers, but this is purely an assumption as I have no evidence.
I would love to know if you have found any further information since you posted this original message.
Look forward to hearing from you,
Amanda Taylor (nee Dorr)