Robbie,

There is no river Dundee, but as several of us have said, that isn't what "The Banks of Sweet Dundee" is likely to mean anyway. It is likely to mean "the slopes, earthworks or riverbanks located in the burgh of Dundee."

As for your other question, I see no reason to assume it did not originate on a broadside. You suggested music-hall as an origin, but broadsides of this song were already being printed in the era that saw the genesis of the music-hall (1819-1844). So if it ever was a music-hall song, it made the jump almost immediately to a broadside anyway and became a broadside song.

It's possible that the song comes from an earlier time, and was just committed to paper in the 19th century, as you suggest, but I doubt it. As Joe says, it has the style of 19th century broadsides, not earlier folk ballads. Also, in the case of older songs, we tend to see more variation in the oral versions that survive. Think Gypsy Laddies, which is only demonstrably about 100 years older, but which we find with opening lines as varied as

Three Gypsies Came to Our Hall Door

Blackjack Davey Came a ridin' through the woods

'Twas way out in New Mexico along the Spanish line

There were seven yellow gypsies and all in a row

etc., etc.

We see little of this variation in "Banks of Sweet Dundee," so I would suspect it was just what it appeared to be: a broadside song.

I guess the question that might occur to me is, what about it makes you feel it's older?