Mudpack is exactly right; those little marsh boats are not appropriate for big water. Use a real layout boat for this. The big-water seaworthiness comes from a combination of things:
--The deck, which slopes down to the water, or nearly so, needs to be long enough, or wide enough, to break waves as they try to board the boat. Usually, the boat rides up and almost over each wave, but the very top of many waves will break onto the deck, keeping the deck awash. That, in itself, is a good thing, because it makes the boat harder to see.
--The second feature is key; A cockpit coaming surrounds the boat's cockpit to stop these broken wavetops from flowing into the cockpit, diverting them back onto the deck from where they run harmlessly back into the lake. Usually, it is made of canvas, and the height is usually adjustable so is can be kept just high enough to do its job without presenting a higher profile than is necessary.
--Typically, the side decks are fairly wide, preventing the boat's occupant from getting too close to the side and causing the boat to capsize. Most layout boats are incredibly stable and solid feeling, as long as the occupant(s) stay fully inside the cockpit.
I have never seen a dog used in a layout boat, although I suppose it could be done. But you'll need a tending boat anyway to carry the rig and set it up. Typically, layout hunting is done with two or more hunters, taking turns with one or two guys in the layout while the other(s) tend the rig, retrieving downed birds, and keeping an eye on the layout.