Mark Gregory has located another gem. This time in a small Tasmanian newspaper in 1851 - a time when Australian republican spirit was on the boil (just before the Eureka Rebellion). The name and tune is as above. I'd like to find the tune to give it a whirl for St Pat's Day. I have asked Lord Google. Any clues?
The lyrics are:

TALLY HO! THE HOUNDS

Come Irishmen ! obey the call,
Of tally ho ! the hounds, sirs,
Whatever your creed or station all,
To swell the joyous sound, sirs ;
For 'tis the cry of low and high,
All Europe in, and round, sirs,
And we have too, the game in view,
So tally ho ! the hounds, sirs.
Chorus.
So tally ho ! and tally ho !
And tally ho ! the hounds, sirs,
For we have too, the game in view,
So tally ho ! the hounds, sirs.

Amongst us long, with subtle tongue,
The Saxon shewed dissent, sirs,
His maxim cool, "divide and rule,"
On plundering us bent, sirs ;
And whilst our jars, and cursed wars,
Of Irish bones made mounds, sirs,
He laid his hands on wealth and lands,
And tally ho ! the hounds, sirs.
And tally ho ! and tally ho ! &c, &c.

He stole our name, he stole our fame,
Our food, our arms, our arts, sirs,
Our Parliament away he sent,
And broke our noblest hearts, sirs ;
And whilst by theft, of nil bereft,
His war dogs stalk around, sirs,
Coercion bills, must heat our ills,
Then tally ho ! the hounds, sirs.
Tally ho ! and tally ho ! &c, &c.

Oh ! Irish Peers, what rapturous cheers,
Would greet you if at last, sirs,
With heart and hand, you'd aid your land,
Her slavery off to cast, sirs ;
If landlord too, and farmer's you,
With peasant's bold were bound, sirs,
With joy I'd die, or join the cry,
Of tally ho ! the hounds, sirs.
Tally ho ! and tally ho ! &c, &c.

My orange friend, let discord end,
Between you and your neighbour,
You'll suffer more from foreign shore,
Than from a papist sabre ;
Ascendant's stuff, there is room enough
For all on Irish ground, sirs,
Then share the toil, and share the spoil,
Sing tally ho ! the hounds, sirs.
Tally ho ! and tally ho ! &c, &c.

To close your ranks in one phalanx,
One firm unbroken band, sirs.
And we shall soon hail freedom's boon,
Illumining our land, sirs ;
Then arts shall thrive, and trade revive.
Our glory shall resound, sirs,
And happiness our Isle shall bless,
Then tally ho ! the hounds, sirs.

Chorus.
So tally ho ! and tally ho !
And tally ho ! the hounds, sirs,
For we have too, the game in view,
So tally ho ! the hounds, sirs.