One of the commonest floating verses is 'little girl dressed in blue (red).

Frankie Child, you will find many posts here at Mudcat where the terms are used mistakenly; that is why I quoted the 'Whither Zither' comment in some detail.

Where or when these terms were first used with these definitions, I don't know. J. E. Lighter, 1994, "Historical Dictionary of American Slang," vol. 1, does not note floater with regard to musical verse.
In prison slang, a 'floater' is a magazine or other article that 'floats' or is smuggled from cell to cell (noted in print in 1933, OED). This comes close.
As used in music, 'floater' is not in Webster. Unfortunately, vol. 3 of Lighter's Dictionary, which would include 'Z', has not yet been published. I can't find that 'zipper' with regard to verse has been included in any of the major dictionaries.