Thanks, TheRamblinReilly. I hope you can find the composer.

I just looked at the video link page again and realised that I had not clicked the reply links so there were some replies to the questions about the name of the tune.

These are the suggestions:
Paddy Dunn's
Paddy Cronin's Hornpipe
or "A revamp of Paddy Cronin's Hornpipe"
Charles Haxell hornpipe

In the second part of the tune where the banjo(?) joins in it reminds me very much of some of the traditional tunes gathered in Australia by John Meredith and Hugh Anderson from a lot of older bush musicians and a large number of those tunes were played for bush dances.