So "Great Grandfather time" would date the song back to the mid 19th century?

First time I ever heard of the Black Ball Line ever transporting convicts. The ships did have a prominant black ball logo on their mains'ls. According to Full Hold & Splendid Passage by Bill & Gene Bonyun, the Black Ball Line of packet ships was established in 1817 by a group of New York merchants and ran only from Liverpool to New York. Maybe there was another Black Ball Line that went out to Australia. Anyone got more clues?