Just discovered this one: MY LITTLE KITTEN SUSIE, sung by Lonnie Johnson on her album "Losing Game," originally released 1960. This is true blues; it doesn't seem the slightest bit ironic or cute. There is a sound sample at Barnes & Noble

... ev'rything go wrong.
Yes, she's my doctor when I'm sick. She's my comfort when ev'rything go wrong.
She's my little kitten Susie. She has my true lovin' till I'm dead an' gone.

She knows when I'm worried....