Well found, Monique; from the Wikimedia we now learn that

1. Catharina van Rennes published the song with an original piano accompaniment, of good craftswomanship, thus fit for a "salon" as mentioned in the other thread. This makes me suspect that "En over de weiden" also had such an accompaniment, of which both songs were stripped later by education officials,
2. the lyrics are officially declared to be translated from Standard German, presumably by herself or her husband etc., thus it is not overly surprising that Peter never heard the song before,
3. she fails to mention the poet Friedrich Güll (see my first post), so does probably her direct German source. The poem may well have been considered "folk" in German-speaking areas (who knows more?), and, as I wrote already, there must have been older tunes for it.