So, got a response from the kind people at the Celje Regional Museum and they provided a high resolution picture of what I see as a most historically interesting airguns. Perhaps most important, is that it is marked "Cortina d'Ampezzo" which is the hometown of Bartholomew Girardoni. This almost certainly is one of the oldest known Tyrollean airguns. It almost certainly pre-dates the M-1780 Austrian military air rifle. I would venture to say that this air rifle design is what Girardoni built his design on. So, we're talking early, maybe circa 1750.

Some more info:
total length 910 mm,
length of gun barrel 458 mm,
caliber 9,8 mm

The large flats on the barrel suggests to me that this single shot was loaded by unscrewing the barrel and carefully placing the shot in the breech.

Cortina d'Ampezzo w- info by Dean Fletcher - Photographer - Portland, on Flickr