Eggs in the EU are regulated under Verordnung (EG) 853/2004. Especially 5.1 is or relevancy :
5.1.
"Eggs" means eggs in shell - other than broken, incubated or cooked eggs - that are produced by farmed birds and are fit for direct human consumption or for the preparation of egg products.
However, Austria had a specific regulation on duck eggs, that incorporated special rules until 2006:
Verordnung des Bundesministeriums für soziale Verwaltung vom 7. Mai 1947, betreffend den Verkehr mit Enteneiern
StF: BGBl. Nr. 118/1947
Präambel/Promulgationsklausel
Auf Grund des § 6 des Gesetzes vom 16. Jänner 1896, R. G. Bl. Nr. 89 ex 1897, betreffend den Verkehr mit Lebensmitteln und einigen Gebrauchsgegenständen, wird verordnet:
§ 1. Enteneier dürfen nur nach Maßgabe der folgenden Beschränkungen vorrätig gehalten, feilgehalten oder sonst in den Verkehr gebracht werden:
a) Enteneier müssen die mit deutlich lesbarer, in unverwischbarer, kochechter, nicht gesundheitsschädlicher Farbe angebrachte Aufschrift
Entenei!
Kochen!
tragen. Die Kennzeichnung muß in Umrandung mit lateinischen Buchstaben von mindestens 3 mm Höhe aufgedruckt sein;
b) An den Behältnissen, in denen Enteneier feilgehalten werden, muß an einer gut sichtbaren Stelle auf einem mindestens 20 cm langen und 15 cm breiten Schilde die deutlich lesbare Aufschrift
Enteneier!
Vor dem Gebrauch mindestens 8 Minuten kochen oder in Backofenhitze durchbacken!
angebracht sein;
c) In Geschäftsräumen und Verkaufsständen, in denen Enteneier feilgehalten werden, ist an gut sichtbarer Stelle in der Nähe der feilgehaltenen Enteneier ein mindestens 24 x 30 cm großes Schild anzubringen, das die deutlich lesbare Aufschrift trägt:
Enteneier dürfen zur Verhütung von Gesundheitsschädigungen nicht roh oder weichgekocht verzehrt oder zur Herstellung von Puddings, Mayonnaise, Eierspeisen, Spiegeleiern, Pallatschinken, Omeletten usw. verwendet werden. Sie müssen vor dem Genuß mindestens 8 Minuten gekocht oder beim Kuchenbacken in Backofenhitze völlig durchgebacken werden.
The text prescribes a very precise marking that has to be mounted on the eggs and close to them. Without such a marking, it was illegal to sell eggs from ducks.
There is no more specific reasoning given in the Päamble or main text of this 4-section law, however, the prescribed text says that there is a health reason and to prevent health damage, they demand to cook the eggs for at least 8 minutes, and their products need to be thoroughly cooked as well. It's not permitted to create raw egg products from them, such as Mayonaise.
The Präamble at best indicates, that a law regulating (among others) duck eggs has been enacted first in 1896, and that this law was its successor.
It itself was succeeded by the Lebensmittelsicherheits- und Verbraucherschutzgesetz - LMSVG, however I couldn't spy if or where a similar regulation was in that law but that it replaces the old regulation.
Local regulations?
There might be local regulations for the market that also might cut into it. Usually, market stalls need a market license, which is given for specific goods. For example, my local market has a trader that has a permit for "fruit, vegetables, and salads", but they do not have a permit for any meat products, eggs, or baked goods. Another similar seller has one that is larger by the entry "chicken eggs". It's illegal for the first to have any chicken eggs on display or on offer, but not for the second.
However, it is often very hard to get those local regulations or licensing schemes anywhere else but at the local market inspector (Marktmeister), their office or town hall. By using the market regulations, they can enact a local de-facto ban on such products on the market. However, that's mostly smaller local markets.
Luckikly, Vienna has its own market office, and can be reached at +43 1 4000-8090, their regulations can be found here. It bans cage-farmed eggs in §5, but does not have specific regulations for Duck eggs. However, in applying for a market stall, the form requires you to describe what types of goods you want to sell, and not listing duck eggs and then selling them could be a violation of the market license you got, depending on how strict the market inspector is.