You have given the origin of the name of the city and county of Derry in Ulster. It is likely that there are other languages that also have words that are pronounced the same way as well. Nevertheless, this interesting coincidence has nothing whatsoever to do with the word that appears in the children's song. That word, like the "hey-nonny-nonny" that Shakespeare used in the same way, is nothing other than what the OED describes it to be, as mplsray was kind enough to transcribe above: "A meaningless word in the refrains of popular songs.""Derry" is a word and it does have meaning, just not in English. The word "derry" is the anglicization of the Old Irish Gaelic word Daire (in Modern Irish Gaelic Doire) which means oak grove and/or an area densely wooded with oak trees. Its a topographical term just like Dell which is a small wooded valley.
I just want to explain that the anglicization of Irish daire/doire to derry was not just done in the case of Londonderry. There are hundreds of places and townlands throughout the whole of Ireland that are named Derry or whose name includes the word derry. These places and townlands are not named after Londonderry. They are so named because at one point in their history their original local Irish name included the geographical toponym daire/doire. Quick example, I know of six places named Derryfadda which originally were Doire Fada (which in Irish Gaelic means long oak grove).given the origin of the name of the city and county of Derry in Ulster.