Mull for a day

West Coast Motors packages a one-day tour to Mull and Iona (basically two ferry tickets and a bus ride back and forth across Mull), so you should be able to manage it yourself by using the same CalMac ferries. I'm not familiar with Duart Castle; I don't know how much time a reasonable visit would require. However, it's not terribly far from the ferry port in Craignure where the Oban ferry docks. Now, how long it will take you to get your car off the ferry I have no idea--I was a foot passenger and paid no attention to the vehicles. I think you need to make a reservation for the ferry to Mull; I booked the West Coast Motors tour a day in advance as a foot-passenger, and I'm sure a reservation is even more critical for a vehicle.

The CalMac website says special permission is needed to take a car to Iona, so I think you'll need to travel as foot passengers to Iona. That island is quite small; it doesn't take long to walk to the abbey. The ferry to Iona departs from Fionnphort on Mull. I imagine there's parking there, but again, that's not something I took note of. The CalMac website should have information about that. I'd guess a reservation is important for this second ferry, too.

Check both ferry schedules carefully to see whether visiting the castle makes more sense before or after you travel on to Iona.

You may see references to a three-island tour including Staffa. I read very recently that Staffa is closed now for some reconstruction, so it appears Mull and Iona is what you should plan for, as per your original intention.

If for some reason you want to take the bus rather than your car between the two ferry docks on Mull, the West Coast Motors bus schedule on Mull is here: https://www.westcoastmotors.co.uk/services/WCMO/496

Another source for bus schedules (which should show the same results) is here:
https://www.travelinescotland.com/

The town of Tobermory on Mull is attractive and worth a visit, but it's not on the way from Craignure to Fionnphort. I am somewhat doubtful you can get a good look at the castle, see Iona and also visit Tobermory in a single day, but it might be possible. Do make a plan for lunch. I'm not sure there's more than one option on Iona, and I think you'd need to make a reservation in advance to get a table there. (Be careful about those ferry schedules!)

Ferry services are run by Calmac. It is possible but I think you will find you are short changing yourself unless you catch the first ferry from Oban. That's 6.45 on a Monday which gets you to Craignure at 7.31. Tuesday to Saturday it is 7.25 which gets you to Craignure at 8.11. It will take you an hour to drive to Fionnphort. Iona is car free (only locals are allowed to take a car there) . You will need to leave your car at Fionnphort (there is parking) and catch the foot ferry (regular service) across to Iona. It is a 10 min crossing and another 10-15 inute walk to the abbey. This opens at 10 am. Allow 1-2 hours for a visit and don't miss the museum with the crosses. You need to allow 1-2 hours. You won't have time for much else - grab a quick lunch before catching the ferry back to Fionnphort.

It will take another hour to drive back to Duart Castle You should arrive by 2.30 which will give you 90 minutes for the castle which shuts at 4pm. There is a ferry back at 5.10pm. The next one is either 6.30 or 6.50 depending on day.

If you are walkers, you could easily spend a day exploring Iona. Other things to do on Mull - Tobermory is a lovely small town of brightly coloured houses. It also has a distillery. Do the drive out to Calgary . Just relax and enjoy. Mull is a very special place, as is Iona.

Make sure you book the Oban Craignure ferry well in advance as it does get busy. You don't need to book on the foot ferry to Iona.

Wasleys has it covered. If you are taking a hire car over, check you are permitted to take it on a ferry.