So we now know that Benjamin Bowater came to Australia with his son, Joseph. Both were miners and they were headed for the large coal mining area around Maitland. When Benjamin died, they were in Wallsend which was a coal-mining town, newly created in 1860 by the Newcastle-Wallsend Coal Company.
The fact that they went directly to Wallsend from Melbourne within a few days of arriving, makes one think they must have had work pre-organised. Perhaps they had been promised employment in the new company. Benjamin may have been old enough and experienced enough to be taking on a foreman position. Experienced coal miners would have been required in setting up a new mining company. Was the plan for the rest of the family to follow them to Australia? Anyway, we know that that never happened.
It looks as if the son Joseph stayed on in Australia, married and had a family. There is a Joseph Bowater who was in Victoria (Ballarat), and then later in Queensland (Chaters Towers) where he died in 1911. His wife was Sarah Ann Wimble.
