We sailed when my third was 6 months and he was very very easy. He didn't sleep through the night (ugh), but my husband took him during the day so I could nap. It worked great. He napped in the stroller and was pretty content to sit in his high chair at dinner. When he got fussy, I nursed him. We actually cruised twice for a total of 15 days right when he turned 6 months. We happened to have friends on the first cruise and the mom was delighted to hold the baby whenever I needed her to at dinner.
Next month we are sailing again and he will be 2.5-ish and kid #4 will be 6 months, so exactly your situation (well, OK, plus two more kids, but they are 9 and 12, so they basically take care of themselves on a cruise

). A friend of ours is coming along and she loves my kiddos, so she has offered to watch the baby or the toddler on occasion so I can nap again. Naps are my current life goal right now, as a homeschooling mom with four kids

. We also took a road trip when kid #3 was 1.5. We ended up leaving that trip a day early, driving home overnight because the kid wouldn't sleep. 1 year old was a challenge compared to 6 months!!! Ha! But anyway, we travel. It's what we do. I had two surprise babies a little later in life (I'm 38), so I'm not putting my life on hold any more than I have to. And for me, I'll either be home with four kids, cooking all the meals, cleaning up after 6 people, and teaching the bigs and chasing the littles...OR, I can be on a cruise. It's a no-brainer.
All that said, we can't afford
DCL anymore (especially now that we are 6), so we will be on the Freedom of the Seas. It's a bit different, but they also offer child care for littles, so we will make it works.