No. You need to go to a Doctor who is on the list for where you are exchanging your licence other than your normal doctor. This is done on purpose to ensure that doctors are not placed under duress to sign someone off as fit to drive.
Lists of doctors can be found for the following regions:
- Lower Austria/Niederösterreich
- Tyrol/Tirol | Innsbruck
- Upper Austria/Oberösterreich | Linz
Doctors on this list are officially mentioned as:
sachverständige Ärzte gem.§ 34 Abs.1 Z 2 Führerscheingesetz 1997
H/t to Hendrik Bower for these links.