That's one Pretty Caroline, yes; a lot of broadside editions were published by various printers, and you can see several at Bodleian Library Broadside Ballads:

Pretty Caroline

The set mentioned earlier, noted by Cecil Sharp, is the broadside song. We don't know, though, if the song noted by RVW was a version of that or something else entirely; or which was used in the suite. We'd need to compare the tunes for a start. Mrs Powell's Pretty Caroline has never been published as noted, so far as I know, so it would be necessary to check the MSS to see what the song was; if any words were recorded, that is.