Our boy, how's just about to turn 2, was out on the boat at 11 days old. Slept mostly, only opened his eyes twice, when the engines came on and then again when they rev'd up to get on plane. The first season was easy as that's when they're in the 'potted plant stage'. As in, you set the infant carrier down somewhere and that's where they stay. The second season wasn't as easy. He wasn't mobile enough to be sure of himself but wanted to be active. Now that he's just about 2 this third season is going a bit better. It'll probably be until next season that he's able to take a bit of direction and not require constant handling. Already split the inside of his lip slightly because of bouncing off the seat onto the deck. Seems to have served to teach him that Dad's advice about no jumping might be worth following... He now says 'no jumping' when seated there.
We've had great luck using a 'PeaPod' tent as a place for him to sleep. The mid-cabin berth is great and the curtains make it dark as a tomb. The tent keeps him safe in one place. But you won't be needing that until at least next season.
Meanwhile, take care about the heat. Infants can't regulate their own temp as effectively, so you'll want to make sure he doesn't get too hot. Obviously sunscreen is recommended, but so is avoiding being out in direct sunlight. When you're anchored out the swinging of the boat will make it hard to keep him in the shade. We found a small traveler's umbrella worked perfectly to give us adjustable shade for him.
Next winter look into
http://www.infantswim.com for lessons. Basically teaches them how to come back to the surface and float on their back. Our boy took it at about 9 months and did well with it. He took the next course this year too. Well worth the effort. It's not about 'swimming' per se, but about 'not drowning'. You will, of course, still have to keep an eye on him ALL the time.