Except for the "kitty alone" phrase, I don't see any connection between this and any other "kitty alone" songs. I'm tempted to think it is a Joe Carter original.

Joe and Janette Carter recording: https://www.youtube.com/watch?v=N9iUHAI-SPU

also this treasure (same, but better transfer): https://www.youtube.com/watch?v=pWEV8SJeqV4

Here's my transcription of "Kitty and I" from the Joe and Janette Carter recording. It's almost the same as what Richie posted above.

KITTY AND I
(Joe Carter)

Tomorrow night, I just can't wait
Me and Kitty's got a date
Kitty alone, Kitty alone
Kitty alone and I
Promenade and do-se-do
Cheek to cheek and toe to toe
Kitty alone, Kitty alone
Oh, Kitty alone and I

You ought to hear* her clap her hands
When they play old Sally Ann
Kitty alone, Kitty alone
Kitty alone and I
Take your money if you bet
Never miss a single set
Kitty alone, Kitty alone
Oh, Kitty alone and I

Dance all night till break of day
Don't care what the old folks say
Kitty alone, Kitty alone
Kitty alone and I
Promenade and do-se-do
Cheek to cheek and toe to toe
Kitty alone, Kitty alone
Oh, Kitty alone and I

If she would only marry me
Man,** how happy we would be
Kitty alone, Kitty alone
Kitty alone and I
Teach our kids to dance and play
Driving all our blues away
Kitty alone, Kitty alone
Oh, Kitty alone and I

Tomorrow night, I just can't wait
Me and Kitty's got a date
Kitty alone, Kitty alone
Kitty alone and I
Promenade and do-se-do
Cheek to cheek and toe to toe
Kitty alone, Kitty alone
Oh, Kitty alone and I


*alt: "see"
**alt: "think"

Joe Carter doesn't repeat the first verse at the end, but I like it there.

---

And Ed Trickett did a recording on Folk-Legacy:
https://www.youtube.com/watch?v=xDkGVSagKTk

Here are Ed's notes:

KITTY AND I (Joe Carter)
Side 2, Band 4.
A composition by Joe Carter, son of A. P. and Sara Carter of the original Carter Family. A recording of this tune can be heard on County 706: Joe and Janette Carter. On the original recording, fiddle and guitar are featured. A carpentry foreman, to whom music is only a sideline, Carter lives in Hiltons, Virginia, on a hill overlooking the home place of A. P. and Sara.
Ed - guitar, Cathy - banjo