When we sailed Carnival DREAM last year, my DD was 4 and my DS was 2.5.
We had a great time. I'll give you my recount - taking it for what its worth, every 2 year old is different, and you know your child best.
I don't recall that carnival allowed swim diapers?? DIdn't matter for us as he was potty-trained, but I'd double check this if I were you.
A few things (in relation to DREAM). Both kids were too short for the water slide, unfortunately, this was selectively enforced. They used the water slide for the first half of the cruise, and then by Day 4 or 5 they were turned away. Wanna make a little girl cry????????
DD loved Camp Carnival. DS - not so much. He didn't want any part of it, and usually within 30 minutes of dropping him off, we'd be paged to pick him up again.
DD loved the shows. DS not so much. He was good though and generally grabbed a nap during the shows.
They both sat through dinner in the MDR with no problems.
THey both LOVED mini golf. We played a few times each day.