Cookie let down

So my husband found a recipe for Trefoils cookies. I thought I would try to make them with gluten free flour. The recipe was simple and easy:
2 sticks of butter
1/2 cup sugar
3/4 teaspoon salt
pinch of ginger
1/2 teaspoon lemon zest/ optional
2 cups all-purpose flour

I followed the directions closely and mixed the ingredients just substituting with gluten free flour. The dough looked great! I thought to myself these cookies will be great! I rolled out the dough and cut them with a cookie cutter and placed them on a greased cookie sheet. I put them in the properly heated oven and set the timer. 10 minuets later I checked on them and they were not browning yet. So I left them in there for 2 more minuets. When I came back to check on them they looked like 4 inch flattened piles. I took them out and tried to scoop them off with a spatula and they crumbled badly. They looked like a pile of sand. At this point I am thinking, I know how to bake. I know how to make cookies. What went wrong! Why are these cookies nothing more than crumbs!
Perhaps I didn't make them thick enough I thought so this time I just rolled the dough into 1 inch thick balls and placed them on the sheet and popped them into the oven. I left them in the oven a little longer to cook as well. About 15 min. They came out looking great! I thought yes, finally some good cookies. I took my spatula and started to take the cookie off the sheet..... crumble...crumble...crumble... Ah! What in the world. I managed to get about 5 cookies in tack onto a plate. I thought getting them off the cookie sheet was a challenge,  then I tried to eat one. Oh, boy!

The best I can figure is that flour has gluten, which holds and binds the goopy mess we call dough. Yes gluten, the very thing that makes pasta elasticy, and streatchy so you can make the pasta. Yeah, the very thing I am allergic to. It isn't in the flour I used. And then there's eggs. They help to bind as well. There were no eggs in this recipe. So taking out the only factors that would have held these cookies together, made them turn to sand as soon as I touched them.

Oh man, what a let down.