I know this post is years old but I am hoping that someone will see it. Archibald did indeed die aboard the "Midlothian" and the detail is recorded on a headstone in Rookwood Cemetery, Sydney.
Here is the article:
Archibald Campbell (1829-1837)
Archibald was the second child of Donald Campbell and Mary Bethune and was born at Uig on the Isle of Skye in 1829 and baptized on 7 January 1830. In August 1837, aged seven years, he embarked fromUigwith his parents and siblings on the ship "Midlothian" bound for New South Wales. Unfortunately, on the journey he became ill, died, and was buried at sea.
We have found no record of the cause of death. There were at least 28 young children who died on the voyage, some of which were not named. Archibald's name is not in the official records. The only evidence that exists is a poignant epitaph on the family tombstone at Rookwood Cemetery, Sydney. It reads: "ARCHIBALD CAMPBELL - second son of Donald and Mary Campbell, born at Uig, Isle of Skye, Scotland, died on board the ship Midlothian on her passage from Isle of Skye to Sydney, AD 1837, aged 7 years. Archie was buried at sea."
I hope this reaches those who were inquiring and will be of some value to you.
Sincerely,
AEnone McRae-Clift, Goonellabah, NSW. 2021.