"Parson Upon Dorothy" first appeared in the 2nd ed. of Playford's Dancing Master, 1652. The melody was retained in all subsequent editions....... Also used in Walsh's Compleat Country Dancing Master..... etc.

I could find no tune called "Dorothy" which would fit this time frame.

A lost tune?? Or perhaps also bore another name. For example, the much later song (c. 1800), "Poor Little Adaline" is about a Dorothy-

Dorothy was handsome, her teeth white as snow,
................
And poor litle Dorothy died an old maid,
And poor little Dorothy, Dorothy, Dorothy,
Poor little Dorothy died an old maid.