travel in croatia/slovenia

You'll need to take the coastal road from Dubrovnik to Split. Pick up the motorway at Split (toll road), which is designed like our interstate highways. At Karlovic, you can either continue on the motorway toward Zagreb and connect to the Zagreb-Ljubljana motorway or take the more direct 2-lane road that connects to the motorway at Novo Mesto (about half way between Zagreb and Lubljana). I don't know the exact travel time, but it's a long drive.

Don't forget to buy a vignette (toll sticker) for Slovenia if you don't have one already, you can get it at all gas stations in Slovenia and many gas stations near the border in Croatia. Otherwise your best route is pretty much what Frank suggested, either one would work, either via Zagreb or Novo Mesto. The one over Novo Mesto is usually used to avoid the horrendous traffic jams at the toll plazas around Zagreb, but that's a problem only on summer weekends, so it doesn't apply to you since you'll be driving in late September, however it's a bit longer over Zagreb. I second George's suggestion to check out viamichelin.com for the driving time, much more accurate than Google.

Another useful website is Google Maps. You can get a lot from Google Maps. We went from Split to Ljubljana 2 y ago. The road was an excellent autobahn-class road. The scenery along the coast was great. The drivers are no better or worse than American drivers. If you are going from Dubrovnik to LL, I would strongly suggest a sidetrip to Plitvice Lakes NP. You will be amazed.