Jadrolinija (http://www.jadrolinija.hr/) the main ferry provider in Croatia only runs Korcula to Dubrovnik June - September. If you go to the link above, the first field is date, the second is port of origin and third field is port where you want to go. If you select a date in Oct you will notice Dubrovnik is no longer an option.
However Kapetan Luka (http://www.krilo.hr/en/sailing_schedule.html) does SPLIT - MILNA - HVAR - KORČULA - DUBROVNIK from May to 18th October but it is a passenger ferry only (no vehicles).
Most ferries run a reduced (or no) schedule during winter in Croatia.