We ran into that same problem, and are still dealing with it. My son is 2 and for a while he wouldn't eat anything except for snacks (bananas, apples, etc) between meals. When we would sit down as a family to eat, he would throw a fit or just not eat. I would throw his food away, but two hours later, when my 10 year old would pop some popcorn for a movie, my 2 year old would want to eat all of it!
My living situation isn't ideal at this time, so restricting treats and snacks is very difficult (read 7th circle of hell post if you like), but if I can keep them out of the house, and replace the cookies with things like fresh fruit, he won't have a choice. Fruit cups have lots of preservatives and sugar in them, and are more of a treat than a serving of fruit.
I'm not sure if your daughter is testing you and her boundaries, or maybe she just isn't hungry. Be consistent in whatever you choose to do because at this age, they are looking for a point of weakness to get what they want. Kids are smart!!! Stay strong! And if it gets to a point where your daughter simply refuses to eat for more than a day or two (I mean absolutely nothing by mouth in her stomach), then I would give a call to the doctor, just to see if there is something else going on. Hope this helps!