There are 2 companies operating catamarans between Dubrovnik and Split. One is named Krilo and the other is Jadrolinija. Catamarans going all the way from Dubrovnik to Split stop at both Korcula and Hvar, and both also operate other catamarans that go between the islands and Split. Check all schedules to find the best fit for your itinerary. For Jadrolinija, the catamarans start with the number 9 and you'll need to check both District of Split and District of Dubrovnik to see all the options. The Krilo website is simpler to navigate as they only operate catamarans. I don't believe there's any longer traditional ferry service all the way from Dubrovnik to Split, but there is ferry service for shorter distances. Note that Pullman buses are another option from Dubrovnik to Split, and the views are better than from a catamaran.
If you go straight to Split, you can day trip to Hvar but Korcula really isn't practical. I wouldn't day trip to Plitvice but would instead travel by bus and overnight there on your way to Zagreb (also best for avoiding the most crowded times of day).
I enjoyed my 2-night stay in Zagreb. I found plenty to do, there's a fun pedestrian area in the center of town and the pizza was delicious (right up there with Italy imo). I didn't visit any museums but there are evidently quite a few. You can use the Search box at the top of the page to find prior postings that talk about the museums and other things to do in Zagreb.
My final thought is that 8 nights really isn't enough time to do justice to Dubrovnik, an island, Split, Plitvice and Zagreb, so you may need to edit your destination wish list.