Can't find in songs of C. Dibdin, Jun., as collected in T. Dibdin, 1875, "Songs by Charles Dibdin," nor among those by T. Dibdin in that volume (some miscellaneous songs by others are included). Of course there is no reason to assume that the volume contains all the songs by these three.
The style of Peggy, however, seems unlike that of C. Dibdin, Jun.

There is a song "Peggy Perkins" in the Bodleian, attributed to Charles Dibdin, but unrelated, andalso not in the volume by Thomas Dibdin.