There doesn't seem to be much variation in versions of the lyric in my experience, and a web search doesn't contradict that. Does this suggest it was originally a published song, by a known author, rather than a traditional anonymous song? There was a ship Davy Crockett, and the figurehead still exists in a museum in the US; I dare say there was a Captain Burgess too, which would date the song fairly accurately -- or at least give an earliest date.

Any more info?