Driving from Munich to Croatia

There are no border barriers or crossing fees within Europe. Driving from one country to another is no different than driving from state to state in the U.S. Maybe you are referring to rental car fees for taking the car to another country? They are quite minimal. This summer I paid 30 euros to Enterprise for taking it out of the Czech Republic. No big deal!
The only thing you'll want to consider are drop off fees...if you rent a car in one country and then return it in another, there are substantial fees for doing so. If you take it back to Munich is should be no problem!

Actually, Croatia is not in the Schengen Treaty zone, so there will be passport control at the border with Slovenia.

Sam is correct, Croatia is not (yet) in Schengen so there will be passport checks on the Austrian-Croatian border. All 3 countries (Germany, Austria and Croatia) are in the EU so there will be no customs checks.
There is no border crossing fee, any restriction on free movement would be totally against EU treaties.

• But, if you want to drive on Austrian Autobahns (and it will be a very slow trip if you don't), then you must buy a "Vignette" toll sticker before you enter Austria or at the border. Is this what you mean by "border crossing fee"?
• Where are you returning the car? If you hire it in Germany, and return it in a different country (Croatia) you will be charged a very high fee by the car hire company. If you return it in Germany, you will only be charged a small fee, or no fee at all, for driving it in Austria and Croatia.

Thank you for the replies. We would be dropping off the car in Croatia or Italy. We were told by Auto Europe that not many companies will allow their rental cars to go to Croatia. They do have a few companies that do and to me that sounds like $$$$. We will probably find another alternative to renting a car.

rent a different car in Croatia, that's what we did.

or fly non stop for $125 on a Sunday (takes about an hour)