I came across this information which sounds authoritative though no references are given,

The Diamond sailed to the Davis Strait every year from 1812 to 1819, heading north for 'Baffin Bay where the whalefish blow'. Though this version of the song says she sailed from Peterhead, in fact she sailed from Aberdeen, as sung in other versions.

The whalers would be away for several months, so their womenfolk dressed in their best shawls to see them off. The sailors boasted that when they came back they would be so rich they would burn the whale oil lamps during the day as well as at night.

In 1819 the ships named in this song were waiting in April at a great wall of ice for the pack ice to melt, but the wind changed and they were all caught and frozen in. The sailors knew this might happen and they had put tree trunks inside across the hulls to make the ships stronger. One by one the ships were squeezed flat, but the sailors knew by the sounds that this was going to happen and they could escape onto the ice. They lived in tents made from the sails and burnt their ships' timbers for warmth.

They suffered greatly, but after many months they were rescued and came home. They left the Bonnie Ship the Diamond and the other ships behind, crushed flat by the Greenland ice.
http://www.educationscotland.gov.uk/scotlandssongs/secondary/genericcontent_tcm4555598.asp