You can reach Kočevje by car on the 106 regional road from Ljubljana, which is a good hour away, or about 60km from Ljubljana. The Croatian state border is 30km from Kočevje, Novo mesto 50km and Postojna 70km.
Parking: In the town of Kočevje, there are many designated parking spaces for cars.
E-vignette: Drivers in Slovenia need a e-vignette for driving on the motorways. E-vignettes can be purchased online, at gas stations in border areas of neighbouring countries before entering Slovenia, at gas stations, post offices and in shops in Slovenia, at the branch offices of the Slovenian AAA (called AMZS) and foreign car clubs.
You can see the route from Ljubljana to Kočevje in more detail on the map.
Some car rental providers in Slovenia:
Sixt Avis Europecar Hertz