We sailed out of Barcelona last September. You will be able to make the 1pm flight easily with a 5am docking. Many of our group flew out at noon with a 7am docking,no problem.
We used the cruiselines tour and went to Montserrat. Absolutely do this..what an experience...wish we cold have stayed longer.
I found a lot of advice on "Trip Advisor", including tours.
We spent 2 extra days on Barcelona, and its beautiful,busy city...I would definitely find a tour for a short visit.