See Postcard Depicting the Vienna State Opera House, circa 1900 by Austrian School.

This picture, if one can believe the ca. 1900 attribution, indicates that Sorcha's picture was made before then, before the two equestrian statues were placed on the pedestals at the top front (or that her artist just didn't like drawing horses). A history of the opera house might give an indication of when those two statues were added, which would indicate at least a "latest date" for the original(?).

About Vienna indicates "The Vienna State Opera was one of the first buildings to be built on the famous Ringstraße, between 1861 and 1869 in a neo-romantic style." That doesn't necessarily mean that the two equestrian statues were added by 1869, but it does look like, from the size of the pedestals, that they planned for something "of imposing size" there in the original construction.

A slight "glitch" in the dating, REMEMBERING THE REBIRTH:

Among the most prestigious opera houses in the world, the Vienna State Opera was destroyed by Allied bombs at the very end of World War II. Ten years later it was reconstructed on the original model of 1869. When it reopened on November 5, 1955 with Beethoven's Fidelio conducted by Karl Böhm, it became the symbol of cultural rebirth and the beginning of a new post-war era. This documentary brings together almost all of the main witnesses of the devastating event: Sena Jurinac, who was in the opera house at the moment of the explosion; Elisabeth Schwarzkopf, Wilma Lipp and Waldemar Kmentt, who saw the Staatsoper burning and who sang the first notes at the reopening gala ten years later; members of the orchestra and ballet, who recall the tragic moments of March 12, 1945, the reconstruction period and the early days of the new opera house.

Sorcha's print certainly represents something pre-1945, but the history I've found thus far only deals with the rebuilding of the house.

John