Looks like the 10th edition of Ramsay's Tea-Table Miscellany (volume 1) includes "If e'er I do well, 'tis a wonder", which pushes the date back to 1740, 9 years before The Charmer! Here it is on archive.org

This publication by S. Powell from 1734, while also being listed as the 10th edition, does not include "If e'er I do well". It was also divided up into three volumes as opposed to the above publishing's four. I also couldn't find this book's volume number. It's entirely possible that the song is in a different volume published sometime between 1734-40, but there's nothing on archive.org.