Dun Laoghaire is a tender port, so if you don’t have a ship tour you will need to go to the lounge where tickets are being distributed. I would suggest getting there as early as they open up so you can be toward the front of the line. Elite passengers and those with Princess shore tours get priority for tendering, so if you don’t fall into one of those categories, you could be facing a bit of a wait so the earlier you can get to the lounge for your ticket the better. Your whole party will need to be with you in order to get the tickets. Then you wait in the lounge until they call your group. It’s hard to say how long this will take - depends on how close you are to the front of the line and how many priority passengers are departing early.
Another point, the tender transit into Dun Laoghaire is the longest we have ever experienced - it is a good 30 minute boat ride. So you will need to factor that in as well. I would imagine, if the ship arrives on time and receives prompt clearance the tenders will start running immediately, but depending on your tender group you willl likely have at least a minimal wait time even if you are in an early group so I would not expect to be at the dock to meet your family until 8 - 8:30 am at earliest.