The air force wasn't allowed to be strong enough for much more than air policing.
The 1955 neutrality treaty didn't cap air force size, only armament. Austria wasn't allowed any missiles or rockets (as well as submarines, torpedo boats, sea mines, artillery with range above 30 km and the usual WMDs).
They therefore established first two, later three squadrons with gunfighters and kept a QRA ready beginning in 1966 - keeping scores of gunfighters would have simply been a waste of money, and the Czech/Hungarian/Yugoslav borders are short enough that the QRA could be at any point of them within about 10-15 minutes after an alarm. This was coupled with long-range radar stations that pull tight surveillance on the air space anywhere within about 20 minutes supersonic flight of Austria's borders.
The weapons restriction was unilaterally (!) declared invalid in August 1990, and subsequently Austria bought AIM-9P3 in 1994, as well as Mistral for GBAD around the same time. The switch officially added
"Luftraumverteidigung" (Air Defense) to the Air Force's portfolio, previously the jet aircrafts' functionality was
"Luftraumüberwachung" (Air Surveillance / Air Policing).
Since the signatory powers of the neutrality treaty did not speak up at the time Austria has since kept buying weapon systems that technically violate the treaty - which is still in power.