That bullshit about the plague did not append itself to the little children's singing game until the 20th c.
See the several threads on this rhyme here at Mudcat. There are many versions:
A ring, a ring o' roses,
A pocket-full of posies;
One for Jack and one for Jim
And one for little Moses!
A curchey in, and a curchey out,
And a curchey all together.
Shropshire, 1883, from Opie and Opie, "The Singing Game."

Naow fer land's sakes, don't suggest that the Jim in the verse is Jimmie of crack corn fame, and that the rhyme is descended from an old West African chant that has to do with preparing maidens for deflowering.

Gira, gira, rosa,
Co la piu bela in mezo; and etc.