Who is the author of the ditty (a partial verse): "all along the
backwater, through the rushes tall, ducks are adabbling, up tails
all."  And where was it first published?

Dear epilogue,

Those words derive from the poem "Ducks' Ditty", written by British
author Kenneth Grahame (1859-1932) as part of his childrens' book "The
Wind in the Willows". In that book, the poem - described as a song
there - is recited by the character Ratty at the beginning of chapter
2, 'The open road'.
"The Wind in the Willows" was first published in 1908 by the British
publishing house Methuen & Co., London.

Here is the full text of the poem:


DUCKS' DITTY

All along the backwater,
Through the rushes tall,
Ducks are a-dabbling.
Up tails all!

Ducks' tails, drakes' tails,
Yellow feet a-quiver,
Yellow bills all out of sight
Busy in the river!

Slushy green undergrowth
Where the roach swim
Here we keep our larder,
Cool and full and dim.

Every one for what he likes!
We like to be
Head down, tails up,
Dabbling free!

High in the blue above
Swifts whirl and call
WE are down a-dabbling
Up tails all!


Please follow this link to read Chapter 2 of "The Wind in the
Willows", with "Ducks' Ditty" at the beginning:
http://elibrary.fultus.com/mergedProjects/Grahame,%20Kenneth%20(1859-1932)/mergedProjects/The_Wind_in_the_Willows/chapter_2._the_open_road.htm
Source:
Fultus eLibrary: Kenneth Grahame - The Wind in the Willows
http://elibrary.fultus.com/mergedProjects/Grahame,%20Kenneth%20(1859-1932)/mergedProjects/The_Wind_in_the_Willows/whnjs.htm

Please follow this link if you prefer a plain TXT format version of
"The Wind in the Willows", courtesy of Project Gutenberg:
http://www.gutenberg.org/dirs/etext95/wwill11.txt

Follow this link for a brief biograpy of Kenneth Grahame, at the
Wikipedia Online Encyclopedia:
http://en.wikipedia.org/wiki/Kenneth_Grahame

Follow this link for a more extensive Grahame biography, by Fultus eLibrary:
http://elibrary.fultus.com/mergedProjects/Grahame,%20Kenneth%20(1859-1932)/kenneth_grahame_(1859-1932).htm


Search terms used:
"tall ducks are adabbling"
://www.google.de/search?hl=de&newwindow=1&q=%22tall+ducks+are+adabbling%22&btnG=Suche&meta=
"tall ducks are a dabbling"
://www.google.de/search?hl=de&newwindow=1&q=%22tall+ducks+are+a+dabbling%22&btnG=Suche&meta=
"ducks ditty"
://www.google.de/search?hl=de&q=%22ducks+ditty%22&btnG=Google-Suche&meta=
"ducks ditty" ratty
://www.google.de/search?hl=de&newwindow=1&q=%22ducks+ditty%22+ratty&btnG=Suche&meta=
"wind in the willows" grahame published
://www.google.de/search?q=%22wind+in+the+willows%22+grahame+published&hl=de&lr=&newwindow=1&start=0&sa=N
"the wind in the willows" 1908 "first edition" london
://www.google.de/search?q=%22the+wind+in+the+willows%22+1908+%22first+edition%22+london&hl=de&lr=&newwindow=1&start=0&sa=N
"wind in the willows" Methuen 1908
://www.google.de/search?hl=de&q=%22wind+in+the+willows%22+Methuen+1908&btnG=Google-Suche&meta=
"kenneth grahame"
://www.google.de/search?hl=de&q=%22kenneth+grahame%22&btnG=Google-Suche&meta=


Hope this answers your question!
Best regards,
Scriptor

Very complete answer, and much appreciated...thank you!  DD