Here's some info from Folk Index:

Kitty and I - Carter, Joe (Joe-L)

Lissenberg, Theo. Galax International, Heritage (Galax) 067, LP (1988), cut# 21
Lissenberg, Theo. 49th Annual Galax Old Fiddlers Convention, Heritage (Galax) 700, LP (1985), cut# 15
Trickett, Ed. People Like You, Folk Legacy FSI-092, LP (1982), cut# 10

There's also a Carter Family song entitled, "Little Joe:"

What will the birds do, mother, in the spring
Will they gather the crumbs around our door
Will they fly from the nest to the top of the tree
And ask why Joe wanders out no more

Does anyone have any detailed info on the "Kitty and I" song?

Richie