Digitised newspapers ....

hope you enjoy armchair reading

here's the link to the pdfs for many historic mid 19th century newspapers useful re Australian research. These are not as easy to go through as there's no keyword searchable options, but once upon a time these newspapers were only available in Public Libraries so at least you can get to them from your own armchair now.
http://www.nla.gov.au/ferg/ While the heading suggests 1840-1845, there's actually a wider coverage than that at that link. The Shipping lists were in many newspapers, often dedicated pages in the Commercial rags, and of course, there's a link to browse by subject or by title/year first published.
http://www.nla.gov.au/ferg/issn/14403897.html This link covers 1844-1855, for The Shipping Gazette and Sydney General Trade List.
As you are looking for 1860-1900, the Ferguson resources will at least give you the names of newspapers that were available in the decade before 1860, so a good starting point.
Cheers, JM