Plane to Train in Zurich

Two hours should be OK, it is a very efficient airport, you should be out in well under 1 hour. And you are correct no immigration (intra-Schengen). There is customs, but that is just walk through "nothing to declare".
But, things can go pear-shaped. Easyjet is usually OK, flights in the morning are OK, but they have no slack in their timetable, so afternoon and evening flights can (but not necessarily will) be 30+ minutes late.
Odds: GOOD
1) Are you sure your train is from Zürich Flughafen? I was under the impression that most trains on that route started at Zürich HB and left Zürich heading in a different direction, not via the airport.
2) Seams a circuitous route. Is flying to Munich not quicker?

It is on one ticket and I do change in Zurich. However, that is the last train from the airport that would allow me to make the connection. (It it's allowed, I may take an earlier train from the airport to the main train station.)

Yes, Munich would be easier but the ride from Zurich is prettier. And I'm one of those who likes the journey and don't see trains as just a way to get from A to B. Unless I'm in a rush I choose scenery.

My flight is early morning so I know that will help.

Frank, there are no reservations on trains in Switzerland. As you exit arrivals, look for signs "Bahn/Railway" and just get the first train to Zürich HB, spend the spare time there. Possibly buy food and drink for the journey.
The train from Zürich to Innsbruck is nice. Exiting Zürich sit on the left, you see Zürichsee, then the more spectacular Walensee. At Buchs (the last station in Switzerland) the train changes direction. You then go through Liechtenstein (but you don't stop there!). and then a long climb to the Arlberg pass (long tunnel). Finally along the Inn river valley to Innsbruck. Enjoy!

Yes. did this 2 years ago (at least as far as St Anton) with Saver ticket. Since my flight actually landed early, I confirmed that it was OK to take the first available S-bahn to Zurich Hbf. Stored my bags in a locker and toured the Swiss National Museum across the street before the Railjet departure time.

It's nice to see that even the "experts" need help sometimes:)