Flights

The airport is open even if a certain desk is not--and if they scheduled you at that time, they must plan on your ability to make it.
I would check in online, use a kiosk if you check bags, and do a google check to see what security lines are typically like at that hour.

The Dubrovnik airport is tiny— slightly larger than microscopic! Even one hour would be plenty of time to make your flight.

My one and only experience flying out of Dubrovnik and that of friends traveling with a different carrier is that we stood in lines that were long while waiting for desks to open. Security longs were long. They barely made their flight even after being permitted to move to the head of the security lines. The flights were domestic and we arrived at the airport two hours before flight time to closed checkin counters.

Agree with Kenko.
Getting there too early was pointless, and I'm usually a get to the airport extra early person.