There are two options for ferries from Dubrovnik to Korčula:
You probably have found the time table from Jadrolinija. You are right that they currently don't run their ferry off-season, but only until end of September. But even until end of September, the ferry runs only twice a week, on Thursday and Sunday. October 1st is a Wednesday.
The second ferry option is Krilo, which operates a high-speed catamaran from Dubrovnik to Korčula until October 18th, but also only twice a week on Tuesday and Thursday. If you arrive in Dubrovnik on Wednesday, you would have to stay a night there and take the catamaran departing 16:30 on Thursday and arriving in Korčula 18:25.
When do you arrive in Dubrovnik? Since the bus from Dubrovnik to Korčula also only runs once a day (15:00), there seem to be no possible way to get to Korčula with public transport if you arrive later. The bus takes 3h 15m.
You can also go by bus from Dubrovnik to Orebic (daily at 14:15 except Sundays and public holidays, arrival 16:15) and take one of the frequent ferries from Orebic to Korčula.