We had a cat 11 with 2 adults, a 3.5 yo and a 8 mo old. We requested a crib from our stateroom host and he took care of that. Even with the crib and our double carriage in the room, we had no problem with space. I had previously sailed in a "suite" on the Big Red Boat and the size of
DCL's cat 11 was similar to that. We also found we had plenty of storage space. If we hadnt been able to get a secret porthole room for our next cruise, we would have gotten an 11 again.
As for cruising with a little one, our 8 month old was easier than our then 3.5 yo.

He loved the pool, slept when he needed to, and he loved the attention from the waiters.
Good luck!