This happens to us all the time. Firstly, we use butter, and if you happen to be using butter in your recipe, this can happen to you as well.
I know so many people who actually like the taste of flat cookies, frankly, they taste the same as their “not so flat counterpart. Aesthetically speaking, I think many don’t like the way they look.
I ALWAYS freeze my cookie dough before baking. I actually scoop or ball out my dough in a particular size and then freeze them for 4 to 24 hours. *I really love a cookie scoop-it creates uniformity and consistency as cookies as all cookies end up in the same size. I make sure my oven is FULLY preheated to the temperature for that recipe and I then place the frozen dough balls on a baking tray. Frozen cookie dough, generally bakes with less of a spread.
If you are worried that your cookies will bake flat, then bake just One as a test with the guidelines above before committing all the dough. Also, if you happen to bake on a silicone baking sheet (Silpat-my personal favorite), remember that even when pulling your tray of cookies out of the oven, the heat from the Silicone mat is still “baking” your cookie, so you can pull out a bit before fully baked as long as the center of the cookie does not look raw.
I also think the Silpat allows our cookies to bake evenly and we have had really great success with that.