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After a lovely email chat with Michael at Dooley Car Rentals in Belfast, belfast at dooleycarrentals.com, he confirmed that, "yes, 0630 collection is absolutely grand."
When you book online, and select Belfast Docks (or any other location that have the Meet & Greet Service, you can specify the time you'll arrive. You'll want to include in your booking the ferry line on which you'll arrive, arrival date and time and the dock location.
And for making itself available 7 days a week, and having extensive service hours (nearly every hour of the day and night), it deserves a bit of a promo:
Dooley Car Rentals is family run business with over 50 years of history and experience in the car hire industry. We take pride in providing our customers with a first class service and will always try to go that extra mile. We have 19 Car Rental locations across Ireland and we are one of the few companies that have locations in both Northern Ireland and Southern Ireland.
We have desks in all the major airports arrivals terminals having recently taken a desk in Dublin Airport Terminal 1 and also in Terminal 2.
Here are the Dooley Car Rental locations: