Slovenia, Croatia and Budapest itinerary & transportation

Lot Polish Airlines is your only pick for flying, and they start seasonal flights on June 7th. You'll have to check to see if they're still flying that route in October.
Dubrovnik has a huge number of airlines that fly there seasonally. The rest of the year, very few flights go out of there on a regular basis.

Piran or Koper would probably be the best place to drop your car. Which one depends on which company you're using, of course, as well as your transportation options to Istria. Rovinj or Pula will be the easiest destinations for public/private transfers. Check Go Opti for your options there. For example, you can go from Koper to Rovinj or about 15 euros. It might be a bus or a minivan. We kept our car from Zagreb, through Slovenia to Istria, Plitvice, and then dropped it in Split. It was more expensive to drop it off on the one-way, but not excessively so. That might be a better option for you if you want to avoid busses.

Our our trip last fall, we kept our car until we got to Split. We dropped the car at the airport and took a taxi to town, and that worked very well for us. After our few days in Split, we took the hydrofoil to Dubrovnik, via stops in Hvar and Korcula. We didn't get off at the islands, but it was nice to see them coming into the dock. The service was reasonably priced and a very good way to relax for a few hours en route to Dubrovnik. However, your time frame will require some planning. The hydrofoils are still running at that time, but not nearly as often. In mid-September, when we left Split, there were only 2 choices: 7 am and sometime in the evening which would have had us arriving in Dubrovnik after dark. We chose the 7 am (you need to be at the dock around 6:30), and while it was early to get going, it turned out quite well for us.

In case it helps: There is rail service between Zagreb and Ljubljana, taking about 2-1/2 hours. Buses are more frequent and take about the same amount of time.