From the sheet music at Duke University's 'Historic American Sheet Music' collection:

THE LITTLE BROWN JUG
By Eastburn*
Published by J. E. Winner, Philadelphia, 1869.

My wife and I lived all alone
In a little log hut we called our own.
She loved gin and I loved rum,
I tell you what, we'd lots of fun!

CHORUS: Ha, ha, ha, you and me,
Little brown jug, don't I love thee!
Ha, ha, ha, you and me,
Little brown jug, don't I love thee!

2. 'Tis you who makes my friends my foes.
'Tis you who makes me wear old clothes.
Here you are, so near my nose,
So tip her up and down she goes.

3. When I go toiling to my farm,
I take little brown jug under my arm.
I place it under a shady tree.
Little brown jug, 'tis you and me.

4. If all the folks in Adam's race
Were gathered together in one place,
Then I'd prepare to shed a tear
Before I'd part from you, my dear.

5. If I'd a cow that gave such milk,
I'd clothe her in the finest silk.
I'd feed her on the choicest hay,
And milk her forty times a day.

6. The rose is red, my nose is too,
The violet's blue and so are you;
And yet, I guess, before I stop,
We'd better take another drop.

[The Digital Tradition version has several small differences in wording, a different sequence of verses, and 2 extra verses that are not in the sheet music.

[James J. Fuld, in "The Book of World-Famous Music," 4th edition, says "Eastburn" was the pseudonym of the publisher, Joseph Eastburn Winner, brother of songwriter Septimus Winner.]