I managed to find this song:
The Ric-A-Dam-Doo is a song written about the PPCLI. All was written about the Regiment in WW1.
The Princess Pat's Battalion
They sailed across the Herring Pond,
They sailed across the Channel too,
And landed there with the Ric-A-Dam-Doo
Dam-Doo, Dam-Doo.
The Princess Pat's Battalion Scouts
They never knew their whereabouts.
If there's a pub within a mile or two,
You'll find them there with the Ric-A-Dam-Doo,
Dam-Doo, Dam-Doo.
The Lewis Guns are always true
To every call of the Ric-A-Dam-Doo.
They're always there with a burst or two
Whenever they see the Ric-A-Dam-Doo,
Dam-Doo, Dam-Doo.
The Bombers of the Princess Pat's
Are scared of naught, excepting rats,
They're full of pep and dynamite too,
They'd never lose the Ric-A-Dam-Doo,
Dam-Doo, Dam-Doo.
The Transport of the Princess Pat's
Are all dressed up in Stetson hats.
They shine their brass and limbers too
I believe they'd shine the Ric-A-Dam-Doo,
Dam-Doo, Dam-Doo.
Old Number Three, our company
We must fall in ten times a day.
If we fell out 'twould never do
For then we'd lose the Ric-A-Dam-Doo,
Dam-Doo, Dam-Doo.
Old Charlie S., our Major dear,
Who always buys us rum and beer,
If there's a trench in a mile or two
You'll find him there with the Ric-A-Dam-Doo,
Dam-Doo, Dam-Doo.
Old Ackity-Ack, our Colonel grand,
The leader of this noble band,
He'd go to Hell and charge right through
Before he'd lose the Ric-A-Dam-Doo,
Dam-Doo, Dam-Doo.
Old Hammy Gault, our first PP,
He led this band across the sea,
He'd lose an arm, or leg or two
Before he'd lose the Ric-A-Dam-Doo,
Dam-Doo, Dam-Doo.
The Ric-A-Dam-Doo, pray what is that?
'Twas made at home by Princess Pat,
It's Red and Gold and Royal Blue,
That's what we call the Ric-A-Dam-Doo,
Dam-Doo, Dam-Doo.