The LEGO handmade wooden Duck was released in 1935, long before the LEGO Brick was created. Many other wooden toys were made which can be seen in The Lego Museum, the duck however features in books, LEGO's yearly progress report as well as being made into a model out of LEGO bricks!
I can't find any history of the Ducks being sold on eBay, judging by its age, sentimental value and low production rate it must be a priceless collector's item.
I sent the question to LEGO customer support and they replied:
The LEGO Duck became a classic icon because it was the first LEGO toy ever to be released.
We do not have any lists of where would sell this product however I imagine it would be sold at some antique markets or antique shows so keep a look out!
We do not have any idea for how much it is worth as it is priceless in our eyes and not sold by LEGO any longer. It also does not have a set number which may be why it is hard to find on the internet.
As said by Ambo100, the duck was the first toy produced by the company. This animated short story has a short glimpse of the duck in the design process by Ole Kirk Christiansen.
The film is very interesting as an introduction to the origin of the LEGO company. Click the image below for the full film:
