Typically Cournot equilibrium is taught with identical zero or constant-MC cost functions for the two firms, because that is simpler. I think that's a bad approach. The result of the symmetry is that when you get to the reaction functions and the diagrams, it is very confusing because the two firms look alike. Also, quadratic total cost is an easy way to have rising MC, and the algebra doesn't get any harder.
Also, are the diagrams worth it, especially the Stackelberg diagram? Probably for the sake of teaching reaction functions for use in other settings, but it's really a lot easier to understand with words and equations instead.
I've just tried putting that approach into practice, which also allows integration of multiplant monopoly, in my online MBA course. My example is at http://rasmusen.org/papers/cournot.tex
. My example doesn't have numbers that turn out neatly; I hope somebody else is inspired to improve on it.