Yes, a dummy is a pacifier.

As I was told it (Canberra, Australia, 1979), a set of "pat-a-cake" motions, not the life-stages ones, went with the "ooh-aah, ooh-ah, lost me knickers, can't fnd me bra" component of some forms of the rhyme at hand, which seems to have incorporated it.

The duckpond and the swimming seem to be formulae ni a few versions that have crept in from (or are in common with: "Oh, Jemima, look at your Uncle Jim".

Sanjay Sircar