Thank you for your comments. A relief about the intl driver's license.
I found out that you can buy a 1 week Austrian vignette for EUR 7.60. Is it better to stick to the "old" road via St. Magrehthen or am I better off trying to connect to the A autobahn?
There appears to be a border crossing near Knessem (?) and the Austrian autobahn is just across the border at Altach. However, this short section of road is marked "yellow" or secondary. I guess I can buy a vignette from the border guard or a petrol station on the Austrian side?