Here's the song Bob Coltman mentioned above, but apart from the similarity of the title, I don't see any connection to the song Alabama Mama requested. Instead, this seems derived from one of the Child ballads—darned if I can remember which one.

Transcribed from the sound file at Honking Duck:

WHERE ARE YOU GOING, ALICE
As sung by Grayson & Whitter, 1929

Where are you going, Alice, my own heart's delight?
Where are you going, Alice, this dark and rainy night?
Down in yonder city my attention does remain,
Looking for a young man. Sweet William is his name.

Never mind young William. He will not meet you there.
Never mind young William. He will not meet you there.
Never mind young William. He will not meet you there.
Just stay with me in Greenlands (?). No danger need you fear.

When she heard this sad news, she fell into despair,
Wringing her hands and tangling her hair.
If Willie he is drownded, no other will I take.
Tp lonesome groves and valleys I'll wander for his sake.

[SPOKEN:] Pore little Alice!

When he heard this sad news, he could no longer stand.
Took her in his arms. Little Alice, I'm the man.
Little Alice, I'm the young man that's caused you all this pain,
But now we've met in Greenlands (?) to never part again.