Elan,
First of all, to be clear on the terminology, there's no such thing as and "international driver's license". What you'll need to obtain is an International Driver's Permit, which provides a translation of your home D.L. and must be used in conjunction with your home D.L. I.D.P.'s can easily be obtained at any AAA office for a small fee (about $25).
Regarding whether you "need" an I.D.P., here's the official scoop from the U.S. government on the Czech Republic......
http://prague.usembassy.gov/drivers-licenses.html
Here are some details for Austria....
http://www.gemut.com/car-rental-europe-basics/3763-do-i-need-an-international-driving-permit-idp.html
You'll also need to make SURE that you purchase the highway tax vignette in Austria, and possibly in the Czech Republic as well (not sure). Failure to obtain the tax vignette in Austria can result in hefty fines of up to €1000 or more, which are payable on the spot!
Are you planning to rent the car in Zürich and drop it off in Prague? If so, you'll probably be facing a hefty drop-off fee of hundreds of Euro.
Using well planned rail trips would be faster, more efficient and present fewer potential problems. Your choice of course.