A single-sheet canoe would be a nice size for a child with plenty of space for growth. I personally think a canoe is safer for a child than a kayak, if it flips the child is free of the boat. There several designs on the web.

I did one in 3 mm marine ply and pine a few years back, LOA is 10.4'. I did not finish it due to health problems then got interested in a sailboat build but the KM (an indicator of stability) is 1.6' with 100lb load which suggests good stability and it should also be nimble and agile enough for fun on the water. Like any small boat stability falls with increasing load so it would be a good training craft for a growing younster but it will handle a medium sized adult.

Resistance at 100lb load is very low at 3k - less than 2lb - per KAPER formula so it should be an easy paddle. The sheer plank developments have straight lines so there is no lofting, the bottom is a simple 7.5' x 1' oval using a simple batten for the shape, the bilge planks are cut from the remainder of the sheet. It's a very easy and fast build, no glassing. Fully built but unpainted without seat it is 15 lb. I must finish it one day.

If you have FreeShip I can e-mail you the file, and there is a build blog at http://theancientkayaker.weebly.com/one-sheet-canoe.html which illustrates my building method although there isn't a detailed construction plan available.