As with all questions about trains:
It is possible to include a trip on the Glacier Exress in the itinerary:
The trip will last 14 hours though (start at 08:30 arrive at 22:30). You will have great scenery all the way between Lausanne and Innsbruck. The Glacier Express operates daily until october 15th, seat reservaion is required for an addtional fee. Dining cars are available on the Glacier Express and on the "Railjet" train from Sargans to Vienna.
There is an overnight train Zürich-Vienna that is your best bet if you want to go by train.
Train leaves Sargans at 2237 and arrives in Vienna at 0755. Sargans is 20 mins from Chur by train... However if you can avoid this I would if I were you. The route Sargans through the Arlberg to Innsbruck is very very scenic. And clearly at night - no views! Best to do in the day time. Maybe spend the night in Chur and go on next day.
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