Although unrelated to 'Strawberry Fair' (Roud 173), 'Dabbling in the Dew' (Roud 298) is interesting. It was rather more popular in oral tradition and of greater age, for one thing. It appeared on London and provincial broadsides during the 19th century (perhaps owing its revival to being sung in a stage production by the very popular actress Mrs Dorothea Jordan, but I don't have exact references for that beyond a comment made by Frank Kidson, referred to in ODNR), but was not new then; the Opies quote an anecdotal reference -and text, quoted above by IanC- indicating that it was current as early as 1698, and refer to a broadside of c.1630 in the Pepys collection, 'A mery new jigg ... To the tune of Strawberry leaues make Maidens faire'. Simpson (The British Broadside Ballad and Its Music, 693) prints a tune, 'Strawberry Leaves', taken from an MS of instrumental music. Whether our song was meant by the tune title, or whether the phrase was a common one, isn't certain; but it seems reasonable to guess that an early form of the song, perhaps the original, was intended.

Broadside editions can be seen at Bodleian Library Broadside Ballads:

Where are you going my pretty maid? / The Milk-Maid

The Pepys broadside mentioned can be seen at English Broadside Ballad Archive:

1.258-259 A mery nevv Iigge./ Or, the pleasant wooing/ betwixt Kit and Pegge