The "Nautical Magazine" for April, 1852, gives a list of "the ships lost since the first discovery of a passage through Melville Bay" in 1819.

Twenty ships, by far the largest number, were lost in 1830. Among them are listed "Rattler" and "Resolution."

"Eliza" had been lost in 1822. All three were lost in Davis Strait.

The "Diamond" was lost near or on the coast of Greenland in 1819.

Since the song isn't about the loss of the ships,but about a joyous homecoming, it would seem to date from 1819 or earlier. I haven't discovered just when "Diamond," "Rattler," "Resolution," or "Eliza" were launched.