Travelling from Sorrento to Dubrovnik

We're travelling from Sorrento in Italy to Dubrovnik in Croatia.
I've found the way to do the trip, would love to hear from others that have actually done it...

- From Sorrento we would catch the local train (Circumvesuvianaa) to Naples, dep at 7.22am and arriving at 8.27am
- From Naples we'll go with Trenitalia to Bari, dep 10:00am and arriving 14:46
- Boat from Bari doesn't depart to Dubrovnik until 23.59 which means that we have plenty of time to make it from the trainstation to the ferry, maybe even get to walk around town for a few hours and see a few sights.

Is this possible? Has anyone actually done this trip in September?
And.....do I need to purchase the train tickets in advance?

The old city in Bari is quite special. Make sure you don't miss it. It's also a great pity to miss Matera, just inland and the great cityscape of Italy's south. No need to book in advance.