Picking up and returning a rental car at Dublin Airport/Dan Dooley

Collecting your car at the airport on your way north is the smart way to go. I don't recall that the M1 heading towards Belfast had any tolls - it was the M50 that we had to worry about - but best to check with the reps at Dan Dooley who will have the most current information.
You wouldn't enjoy driving around central Belfast either - traffic is murder. Better to just park the car and either walk or bus to the sights you want to see. The Black Cab tours are highly recommended for the neighborhoods most affected by the Troubles.
You might look at accommodations over in the Titanic Quarter - most of them have parking available and from there you can just walk over to the Titanic Experience at your leisure. Suggest getting to there early (before the tour buses start to roll in around 10 AM) or later in the afternoon after they've departed. It's a whole different experience without the crowds.
Might add that there's a HoHo bus stop right across the street from the Odyssey Center - was a great way to see the highlights without the hassle of a car.

Unless you're planning to use the car for something more than just getting yourself from Dublin to Belfast and back it would be easier (and cheaper) to take the train or a bus. Makes little sense to drive the car up to Belfast only to park it for a couple of days.

We are in Ireland now and we also rented from Dan Dooley at the airport. If you travel the M50 you will have to pay a toll by 8:00 PM the day after travel. You can go online and pay the toll or pay it at any gas station. We stopped at a gas station, filled up and paid the toll. Other tolls are paid at an unmanned toll both. Toss your euros in (1.90 mostly) and wait for the arm to go up. The toll booths that we encountered were unmanned so best to have correct change as they do not give change.

We dropped off our car at the airport and took the link bus into Dublin from the airport, was very easy. You of course will be doing the opposite but my advice would be that on the day you go from downtown Dublin to pick up your rental I would take a taxi from my hotel to the airport. The bus route will cruise you around a bit and you will want to be fresh and non stressed as you venture out with you rental car and head north!! The bus was only like 6-8 euro. The taxi from our hotel in the Temple Bar area took about a half an hour and cost 35 euro for my wife and I. For me the long day I had ahead (flight home) and for you, with a drive up to Belfast, seems like the easy way to start the day would be a taxi to the airport to get your rental..they will drop you right at the terminal where the car rental spots are located. We used Hertz and they had a pass for the toll road (we went south and west frm the airport) and billed my credit card...like 3 bucks or so.