Why are my cookies crumbling after I bake them?
Gluten-free flour is not a perfect substitute for wheat flour. Each mixture out there is designed to mostly work in certain kinds of recipe, but not in all of them. And yes, it is perfectly normal for a gluten-free cookie to be crumbly, since it is the gluten itself that holds wheat cookes together. 

I suppose the prepared flour mixture you have is just no good for cookies. Instead of making substitutions in an existing recipe and hoping for a miracle fit, just find a gluten-free cookie recipe (which is likely to use correct proportions of starches and binders, not the unknown mixture you get in the supermarket) and bake that. Troubleshooting substitutions is rarely worth the amount of work you have to invest, and the end result is not the same as without the substitution anyway.