Well, "Ah Poor Bird," is a different round, with its own lovely melody. And the "Peace Round" words were composed by Jean Ritchie (it's published in The Friends Hymnal). The words I know to, "Rose, Rose" are:

Rose, rose, rose, rose,
Will I ever see thee red?
Aye, marry- that thou wilt,
If thou but stay.

Your, "I am an old man" verse sounds like it was based upon a verse from, "The Souling Song:"

The lanes are very dirty; my shoes and very thin.
I've got a little pocket to put a penny in.
If you haven't got a penny, a ha'penny will do-
If you haven't got a ha'penny, it's God bless you!

What you have I would guess, is a medley- probably born around a campfire. Good fun!