We are traveling on a Eurail pass in May. One part of our journey is from Innsbruck to Munich. I thought it would be interesting to make the journey over Zugspitz - coming up from Austria and down through Germany. Is this possible or practical? Would we have to pay full gare cable car for each direction?
First, I assume you are using public transportation, not a car, since, with a car, you would have to come back to the other base station to pick up the car.
Just because the base of the Austrian Zubspitzebahn is in Austria doesn't mean it is directly accessible from Innsbruck. The main rail route from Innsbruck to Ehrwald, the bottom of the Austrian Zugspitzebahn, goes through Garmisch-Partenkirchen Bahnhof, just yards from the German Zugspitzebahn Bahnhof.
I don't know if there is enough difference between the Austrian side and the German side to make this worthwhile. I know on the German side, you can purchase a trip up (or down) the Zugspitze individually. I would assume the Austrian side is the same. The one-way fare is more than half the round trip fare.
At the top, you can walk between the two top stations.
Another option would be to take the train from Innsbruck down the Inn river to Brannenburg, then take the cograil train up the Wendelstein and the cable car down the other side to Osterhofen, then the BOB (Bayrischer Oberlandbahn) to Munich.
Lee's answer I think is well stated and should put you on the right path.