We will begin our trip to Croatia by flying into Venice. We are now thinking about renting a car and driving first to Ljubljana and then throughout Croatia. Is this easy to do, or will we have to rent separate cars for each country?
You can rent a car but you must check what the agency's policy is regarding international crossing. Sometimes it's minimal and they ask for an additional fee or sometimes a substantially higher insurance rate. The most steep fee though happens if you do not return the car in the same country of origin.
Eurocar charged me 300 EUR last time for that. For a simply border crossing, in my case Croatio to Montenegreo and back it was only 5 EUR. Sixt has a detailed policy in their agency about which fees applies which crossing. Also, in their case, you have to mention this when you rent the car because some of their cars are not allowed in certain countries, possibly for legal reasons.
Now, unless you plan to stop a lot between those places, I highly recommend trains for the northern part of the trip. The cost is much cheaper than what you would pay for gaz over the same distance! From Split though we used high-speed catamarans to reach the south and then renter a car after leaving Dubrovnik which is pedestrian only and having a car quite problematic. Slovenia is easy to drive around though. You can rent local cars or use buses for out-of-the-way places and day-trips which will save you considerable money.
Yes, under EU insurance rules a car insurance policy issued in one member state is valid for travel in all others. It's not possible to issue a vehicular insurance policy which is valid for Italy but not Slovenia or Croatia.
If you plan to leave to EU (for example by going to Serbia or Montenegro) you may need to pay more for additional cover.