Hi Geoff, at the present there are no car ferries from Dubrovnik to Sobra nor to any other ferry port on Mljet island. https://www.croatiaferries.com/dubrovnik-sobra-ferry.htm
Mljet is served from Dubrovnik by foot passenger ferries only.
To take your car to Mljet you have to drive to Prapratno and embark the ferry from there.
The drive takes about 1 hour and 15 minutes. https://www.croatiaferries.com/prapratno-sobra-ferry.htm
Here is a mljet ferry map: