Austria issued this stamp (Scott 864) on June 5, 1970. It depicts the organ in the Great Hall at the Vienna Music Academy. 1970 was the centenary of the building's construction. This site gives several pictures of the organ, but does not give a stoplist, nor the name of the builder.
Update as of 4/2011: Reiger has built a new organ within the pre-existing case. They have a specification here. This discussion board reveals that the original organ was by Ladegast, completed in 1872. The new instrument has 84 ranks at a cost of $1.8 Euros. If the board information is correct, the inaugural concert should have been held recently. The work has been going on since 2010.