You asked: Is the "folly-rolly..." part a nonsense thing, like a children's game lyric?"
A short answer is YES.
There have been a number of Mudcat threads on this song.
Put Jenny Jenkins in the Lyrics & Knowledge Search box, press search and you'll not only find the lyrics Brucie found for you via hyperlink but also other lyrics including some with different nonsense words.
You will also find pages for threads and posts about this song.
And Guest Gary.."nonsense lyrics" by definition are 'nonsense'- meaning that they don't mean anything..
Did these nonsense words originally mean anything?