I'm glad to report that in my post of Jan 24, 2006 I was right with my assumption. Today I heard this song in the central Carnival session of Franconia (Franken), a Bavarian province. It was sung by a firemen's band of the Upper Palatine (Oberfranken), another Bavarian province.
They sang in dialect and so fast that I could not understand much. But this is sure: It is about a woman named Kath. The first verse prophesies that she will finally get one, too. The other one tells that she has got one. The chorus I could not understand.
The tune is in a form seldom used outside of Bavaria called Twofold (Zwiefacher) because it consists of two metres. Two bars of three crotchets each are followed by two bars of two crotches each.
I'll try to contact the band (just got their address) and ask them for more information.