Yes there is daily ferry from Dubrovnik via Luka Šipanska to Sobra (Mljet), departs Dubrovnik 14:30, Luka Šipanska 15:20 and arrives in Sobra (Mljet) at 15:50. Going back to Dubrovnik following morning at 06:30
Adam, in first week of April you have two options for day trip to Mljet: either book pre arranged tour or drive to Prapratno and get ferry from there.
Maybe you can consider overnight on Mljet?