We want to take an overnight ferry from Dubrovnik to Rovinj or somewhere on the Istrian Peninsula. Is this possible? If so, what company? (In April)
No ferry for that stretch.
Most of the cruises I have read about have a more limited scope, but you might check on a popular cruise website.
See some recent coastal ferry news at http://www.croatiaferries.com/rijeka-dubrovnik-pula-zadar-ferry-service-reintroduced.htm. But a big car ferry can be very slow, so our guidebook researcher doesn't really recommend it for long distances.
Although in the announcement has been made that the ferry will be reintroduced, the operator doesn't show it on their website. Jadrolinija.hr.
Schedules for all other sailings are available online. It maybe that for this year, it won't be reintroduced until the summer.
If I were you, I would have a back up plan.