I haven't cruised on
DCL, but we took our first cruise when my youngest was 2 years 9 months. We did not use a stroller, and was glad we did NOT take it. He was able to walk most of the way, and it was easier to carry him when he was too tired than dealing with a stroller.
If you get a state room mid ship, that will help. We took elevators for everything when he was with us, which helps. While the ships aren't that small, you can still walk from end to end in a few minutes at the most. And, it's not like you'll walk end to end, and then back again. You'll walk from one location on the ship, to another, and very rarely will the walk be end to end. Very rarely will you be walking more than a few minutes at a time.
The most walking you do will be embarkation day, when you are trying to explore the ship. You can still do this with a 2.5 yr old, just take it slowly, and stop to look at things if needed. There are plenty of places to sit and rest.