This song is known in Scotland and the north country in England...

Dance to Your Daddy - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World  - Intro Image

Notes

Here's another version:

Dance to your daddy
My bonny laddy,
Dance to your ninny,
My sweet lamb;
You shall have a fishy
In a little dishy,
And a whirligiggy,
And some nice jam.

Dance to your daddy
My bonny laddy,
Dance to your ninny,
My sweet lamb;
You shall have a fishy
In a little dishy,
And a whirligiggy,
And some nice jam.

Bonny = beautiful, pleasant-looking, smiling
Laddie = young boy
Ninny = child
Whirligiggy = whirligig = a twirling or whirling toy (like a top).

*****

This song is called Dance Tae Yer Daddy in Scots. (You can click the link for the Scottish version.)

Here's another version from The Nursery Rhyme Book, edited by Andrew Lang and illustrated by L. Leslie Brooke (1897) - this seems to be a variation of the Scottish version at the link above:

Dance to your daddy,
My little babby*;
Dance to your daddy,
My little lamb.

You shall have a fishy,
In a little dishy;
You shall have a fishy
When the boat comes in.

*Baby

Dance to Your Daddy - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World  - Comment After Song Image
Dance to Your Daddy - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World 1
Dance to Your Daddy - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World 2
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Thanks and Acknowledgements

The 1st version comes from The Real Mother Goose. The 2nd version and the illustration come from Harry's Ladder to Learning (1850). The 2nd illustration comes from The Real Mother Goose (1916), illustrated by Blanche Fisher Wright. The 3rd illustration is from The Little Mother Goose (1912), by Jessie Willcox Smith.