Thank you all very much for your help. The Moreton Bay registers were very helpful. Only two John Andersons there! (and one of them arrived too late to be him.)
The John Anderson on Baring 2 that you mention is the one I'm looking for, and to top it all, Ken Lamb has cross referenced all those convicts with the correspondence from the commandants and one of his (Ken Lamb, not the Commandant!) spreadsheets even mentions Anderson as the scourger.
I didn't know anything about him before except the date of his apointment in Moreton Bay and that he also worked as a waterman for Capt. Logan.