These aren't serious endorsements, but it has been done...
(And I know I've seen a Scamp
trailer on a floating platform but can't find a photo.)
Coming from the boating world, I think a lot would depend on which waterways and what weather you used them in. There are plenty of "real" boats made that are not "seaworthy" but are still okay for their intended use. That is to say that even "real" boats are not necessarily all suitable for all waterways and conditions - far from it. So you need to either only cruise the waterways/conditions that are suitable for a given craft; or, conversely, build or buy a craft suitable for the waterways and conditions you want to go out on.
There are stability calculations that qualified people can make.
You might also like to find the book, "Handmade Houseboats," as that is really what you'd be doing (whether the "house" be a camper or not) and there is a lot about how to make the hull, stability, etc. in the book. Also lots of great photos and drawings.