Jeff, I can't say about your Italy plans, but regarding the rest:
1. Check with the rental agency of your choice if you can take the car from Italy to Croatia. And keep in mind you won't be able to leave them in Croatia, but take them back, so you'll have to fly back from Italy.
2. How on Earth do you plan to get from Venice to Kornić in 4 hours? :) If you make it in under 6, I'll be amazed. It'll be high season all around, you can expect very busy roads and border crossing (Slovenia-Croatia). Then probably all the way to Krk. Keep in mind the highway through Rijeka is used as Rijeka's bypass, almost a regular city boulevard and it might be packed, too. Then you need to get off of it around Bakarac area and use single lane road to reach Krk. After that it's again a single lane road to your destination. With thousands of tourists with caravans. :)
You might get lucky, you never know, but you might end up driving for more than 6 hours. Depending on many unforseeable variables.
But once there... Well, that's something else. I haven't been to Kornić but I have been in Krk (the island and the city). I think it's amazing. And you could also venture onto Cres and Mali Lošinj for more incredible experinces. One week? You'll love it.
Btw, I have 4 movies from Krk in my MTB Street view series, so you can get some feel of the place, including a short trip to Krk city (close to Kornić). Start with this one and see how it goes - http://www.youtube.com/watch?v=0JOKfDT0phw.