The information posted by Andrea is correct. There is no such thing as an "International Driver's License. The correct term is International Driver's Permit and these must be used in conjunction with your home D.L. These are easily available at any AAA / CAA office for a small fee, and are valid for one year. According to this website, an IDP is compulsory for driving in Austria so you'll need to have one - http://www.austria.org/driving-a-vehicle/ . Each driver listed on the rental form must have one.
If you decide to drive, I'd suggest packing along a good map or preferably a GPS unit. If you have an international roaming plan with your cell network, you can also use a smartphone and Google Maps or whatever. It's not likely your home auto insurance will cover rental vehicles in Europe, so you'll either have to pay for insurance from the rental agency or check to see if one of your credit cards provides insurance for rentals. You may find it helpful to download the free car rental guide from this website - https://www.gemut.com/ . If you have any questions, give them a call on their toll free number or send an E-mail. I've always found them to be very helpful.
Vehicles are usually manual shift, so you'll have to specifically request an automatic. Even with a request, the rental agency may not have an automatic available.
If you'd prefer to travel by road and have someone else do the driving, you could also look at a day tour. This is one company operating out of Salzburg - http://www.bobstours.com/tours.php .
One other option you could consider would be to travel to Hallstatt by train, and spend a few nights there. That would allow you time to see the Salt Mine and enjoy the incredible beauty.
glückliche Reise!