You can buy them already at German gas stations in the border region.

You don't need it for driving from Mittenwald via Garmisch, Linderhof, Plansee, Reutte to Füssen and Neuschwanstein.

You need it for driving on an Austrian Autobahn or State Road, but not on a Bundesstraße (Federal Highway), no matter how wide or how many lanes, or if a dozen pink cows are dancing rumba on the median.

If you stay in Mittenwald, the A12 going east/west from Innsbruck is the closest toll road.

But if you should plan to drive from Mittenwald there is one tricky spot: You can drive to Innsbruck on toll-free roads (does that word even exist?) B177 and B171. But: Where you expect a well marked intersection between the two highways, there is only a lousy sign with "Kranebitten" as destination (an Innsbruck suburb and the airport). But if you stay on the main road and follow directions to Innsbruck at that point you will find the road to merge with motorway A12 (and THAT is where the motorway patrol will get you for driving without the sticker).