International Driving Permit

Is IDP necessary?Only of you are stopped by the police for any reason. Considering the cost of your trip, is another $20 any Problem? Easy to get at any AAA office.

Just get it !!! Will you need it ??? Who knows. But for $20 would you rather have it and not need it OR need it and not have it? There was a posting here earlier from someone who didn't have it, got into a very minor fender scrape and the local police nearly impounded his rental because no one was legally available to drive it away. Someone will post that they have driven for 20 years in Europe and never need it. Proves absolutely nothing. Just get it.

IDP is a country-by-country thing, you need current advice from that specific country about fines or more importantly inability to rent in the first place. Here's one topic https://www.tripadvisor.com/ShowTopic-g294453-i1554-k11820417-International_Driving_Permit_Requirement-Croatia.html
Pay attention to the Slovenia part.
Also recommended on this website https://www.ricksteves.com/travel-tips/transportation/rental-car-requirements

Aside from the issues already raised, some car rental agencies will demand to see an IDP. Which ones? No one knows! I didn't even mean "brands", I meant "agency" desks. I can tell you I was asked for one in Italy in a recent year, from a big brand like Avis or Hertz.

The quote Dirty Harry, "How lucky do you feel?" While the rental companies are nor supposed to rent you a car if you don't have an IDP, they can be very lax about it for two reasons. 1) The guy at the counter will not be in the driver's seat if you get stopped by a cop who can easily decide to impound your car on the spot since you are not properly licensed to drive it. 2) The rental agency has you by THE CREDIT CARD so they can recover all the costs of getting the car returned from impound or even better the costs of any repairs in an accident since your insurance will be voided because you are not a properly licensed driver. Sound like fun??

your insurance will be voided because you are not a properly licensed driver.

This statement has never been substantiated by any post or experience.

I was once unable to rent a car because I did not have an IDP as required. Most likely you'll never be asked, but it is the law and you don't want a trip ruined or altered because of it.

It doesn’t cost much to get an IDP - peanuts compared to the one way drop fee. Just get one.

Have you considered renting in Dubrovnik, returning in Zagreb, and taking a train/bus between them? If you have 4 or more, this is probably not cost-effective. But if you are 2, this might be a very reasonable choice.