People do this, but they generally harvest the down and put it in the new shell.

Aside from the weight of the cotton, you would need to make the nylon breathable - a totally waterproof shell would make the quilt uncomfortable for you, as it would trap all your perspiration inside with you, and while this is a tactic to keep you warm in sub freezing temps you don't want this when you're above freezing. And if you make the nylon breathable, moisture can get in and saturate the cotton, which will then not dry out fast, which is why so many backpacking primers will tell you not to use cotton clothing, especially in winter. Making the entire quilt heavy and wet.

So I would look at various instructions for homemade quilts and harvest the down to put in the new quilt.