There seem to be two unrelated Road to Gundagai poems by Banjo Paterson.

The Australian Poetry Library has Banjo Paterson's poem "The Road to Gundagai" from his 1902 book "Rio Grande's Last Race and Other Verses":

The Road to Gundagai

The mountain road goes up and down,
From Gundagai to Tumut Town.

And branching off there runs a track,
Across the foothills grim and black,

Across the plains and ranges grey
To Sydney city far away.

It came by chance one day that I
From Tumut rode to Gundagai.

And reached about the evening tide
The crossing where the roads divide;

And, waiting at the crossing place,
I saw a maiden fair of face,

With eyes of deepest violet blue,
And cheeks to match the rose in hue -

The fairest maids Australia knows
Are bred among the mountain snows.

Then, fearing I might go astray,
I asked if she could show the way.

Her voice might well a man bewitch -
Its tones so supple, deep, and rich.

"The tracks are clear," she made reply,
"And this goes down to Sydney town,
And that one goes to Gundagai."

Then slowly, looking coyly back,
She went along the Sydney track.

And I for one was well content
To go the road the lady went;

But round the turn a swain she met -
The kiss she gave him haunts me yet!

I turned and travelled with a sigh
The lonely road to Gundagai.

And the Institute for Australian Culture has "On the Road to Gundagai" from Paterson's 1905 book "Old Bush Songs", which is our "Lazy Harry" from above.

On the Road to Gundagai

Oh, we started down from Roto when the sheds had all cut out.
We'd whips and whips of Rhino as we meant to push about,
So we humped our blues serenely and made for Sydney town,
With a three-spot cheque between us, as wanted knocking down.

Chorus
But we camped at Lazy Harry's, on the road to Gundagai.
The road to Gundagai! Not five miles from Gundagai!
Yes, we camped at Lazy Harry's, on the road to Gundagai.

Well, we struck the Murrumbidgee near the Yanko in a week,
And passed through old Narrandera and crossed the Burnet Creek.
And we never stopped at Wagga, for we'd Sydney in our eye.
But we camped at Lazy Harry's, on the road to Gundagai.

Chorus: But we camped, &c.

Oh, I've seen a lot of girls, my boys, and drunk a lot of beer,
And I've met with some of both, chaps, as has left me mighty queer;
But for beer to knock you sideways, and for girls to make you sigh,
You must camp at Lazy Harry's, on the road to Gundagai.

Well, we chucked our blooming swags off, and we walked into the bar,
And we called for rum-an'-raspb'ry and a shilling each cigar.
But the girl that served the pizen, she winked at Bill and I —
And we camped at Lazy Harry's, not five miles from Gundagai.

In a week the spree was over and the cheque was all knocked down,
So we shouldered our "Matildas," and we turned our backs on town,
And the girls they stood a nobbler as we sadly said "Good bye,"
And we tramped from Lazy Harry's, not five miles from Gundagai;

Chorus: And we tramped, &c.