This is an older song than anybody seemed to realize. From the sheet music at The Lester S. Levy Collection of Sheet Music. For those who want to make a detailed comparison, I have boldfaced the differences in wording between the sheet music and the version in the Digital Tradition database.

I WANT TO GO TO MORROW
Words and music, Lew Sully
New York: Geo. W. Meyer Music Co., 1367 Broadway, 1898.

1. I started on a journey just about a week ago,
For the little town of Morrow in the state of Ohio.
I never was much of a traveler, and really didn't know
That Morrow had been ridiculed a century or so.
I went down to the depot for my ticket, and applied
For tips regarding Morrow, not expecting to be guyed.
Said I, "My friend, I want to go to Morrow and return
Not later than tomorrow, for I haven't time to burn."

2. Said he to me, "Now let me see if I have heard you right:
You want to go to Morrow and come back tomorrow night?
To go from here to Morrow and return is quite a way.
You should have gone to Morrow yesterday and back today.
For if you started yesterday to Morrow—don't you see?—
You could have got to Morrow and returned today at three.
The train that started yesterday—now understand me right—
Today it gets to Morrow and returns tomorrow night."

3. Said I, "My boy, it seems to me you're talking through your hat.
Is there a town named Morrow on your line? Now tell me that!"
"There is," said he, "and take from me a quiet little tip:
To go from here to Morrow is a fourteen-hour trip.
The train that goes to Morrow leaves today, 8:35.
Half after ten tomorrow is the time it should arrive.
Now if from here to Morrow is a fourteen-hour jump,
Can you go today to Morrow and come back today, you chump?"

4. Said I, "I want to go to Morrow. Can I go today
And get to Morrow by tonight, if there is no delay?"
"Well, well," said he, "explain to me—and I've no more to say—
Can you go anywhere tomorrow and come back again today?
For if today you'd get to Morrow—surely you'll agree—
You should have started not today but yesterday, you see.
So if you start to Morrow, leaving here today your flat,
You won't get into Morrow till the day that follows that.

5. "Now if you start today to Morrow, it's a cinch you'll land
Tomorrow into Morrow, not today, you'll understand.
For the train today to Morrow, if the schedule is right,
Will get you into Morrow by about tomorrow night."
Said I, "I guess you know it all, but kindly let me say:
How can I go tomorrow if I leave the town today?"
Said he, "You cannot go to Morrow any more today,
For the train that goes to Morrow is a mile upon its way!"

FINALE. I was so disappointed, I was mad enough to swear.
The train had gone to Morrow and it left me standing there.
The man was right in telling me I was a howling jay.
I didn't go to Morrow, so I guess I'll go today.

[p.s. For those who want to know whether the story has any basis in fact: The Getty Thesaurus of Geographic Names lists inhabited places (i.e. cities, towns, or villages) called Morrow each of the following states: Arkansas, Georgia, Idaho, Louisiana, Ohio, and Tennessee—but, alas, none in Australia.]