That is an interesting experiment. How did it go?
One problem might be that stereograms have to be drawn to match the distance between the viewers eyeballs. If the physical distance between a childs eyes isn't large enough (as stereograms are mostly designed for adults) they will not be able to see the image.
To get around the above problem you could print out the stereogram such that the printed version is physically smaller than the version that appears on the screen (perhaps 3/4 of the size). Shrinking the image on the monitor probably wouldn't work, as stereograms depend on every pixel.