"Nursery Rhymes of England," 1846, James Halliwell, has this version (p. 4):

V.
I had a little nut tree, nothing would it bear
But a silver nutmeg and a golden pear;
The king of Spain's daughter came to visit me,
And all was because of my little nut tree.
I skipp'd over water, I danced over sea,
And all the birds in the air couldn't catch me.

Halliwell notes: "The following perhaps refers to Joanna of Bastile, who visited the court of Henry the Seventh." No support provided for this statement.

There are some rhymes about skipping over water; this one may be a compound.