Hi MaryAnn,
The afternoon bus from Dubrovnik to Vela Luka (Korcula Island) passes near Prapratno. You will have about 15 – 20 minutes walk downhill to the ferry port. You should be able to get ferry at 17:00 from Prapratno to Sobra on Mljet.
The next one is at 20:30 which is also the last one to the island.
Instead, it is better and easier option to take foot passenger fast catamaran from Dubrovnik to Pomena (also on Mljet island) and take taxi from Pomena to Sobra. Departs Dubrovnik at 16:30 arrives Pomena at 17:45.
All ferry details are here https://www.croatiaferries.com/dubrovnik-pomena-ferry.htm
To get back to Dubrovnik and get your flight at 10:30 you will probably be better off to overnight in Dubrovnik.