A little more-

I've a little black dolly named Topsy
Who doesn't like sleeping alone,
For Topsy's afraid of the shadows,
In darkness I'm sure there are none.
But Topsy is only a dolly
And doesn't know better you see,
So I just tuck her under my pillow
For I know she likes sleeping with me.

And when the sun shines in the morning
I sing until I know she's awake.
Then I take her right out in the garden
And give her a bath in the lake.

Though I scrub her and scrub her and scrub her,
I can't get her white like me.
But Topsy is blacker than ever
And shiny as shiny can be.
So I'll just pop her under my pillow
For I know she likes sleeping with me.

Taken from one of the versions on the internet. A couple of lines seem to be missing, the verses aren't even. I remember that it was in a children's story and rhyme book that I had as a child. No idea of author or age.