My poor son has anaphylactic allergies to eggs, shellfish, soy, and peanuts, and possibly milder allergies to corn, wheat, and dairy. We're in the middle of an allergen elimination diet to confirm the possible milder ones (they showed up on his blood test, but he eats them regularly with no anaphylactic reaction).
I would suggest looking at paleo and primal recipes. Especially if your child can do eggs, there are some awesome ones out there. Check out the websites of Paleo Parents, Nom Nom Paleo, Civilized Caveman, and PaleOMG, they all have some awesome wheat free (in fact, totally grain free) dessert recipes including lots of excellent cookies. Personally, I find almond flour to be much yummier than wheat. Coconut flour is pretty good too, but can be weird to work with. I personally don't care much for the taste of other gluten free flours (when you go wheat free, you pretty much go gluten free by default, my son has no issue with gluten either, but most wheat free things just are gluten free too), they have bitterness to them, and the texture can be off. Not much, but just enough to dip into the uncanny valley, I think. That being said, if you're in the market to just buy some wheat free cookies, Enjoy Life brand makes some pretty good ones. I buy them at my local grocery store (Kroger), but you can also find them at any natural food store like Whole Foods. I can even get them from my organic food delivery service where I get my milk. I get them mostly for my son, who gets so few treats with all these allergies.
Food allergies suck. I never wanted to be that mom who has to watch every morsel my son puts into his mouth like a hawk, and pack him food for every event. Going to birthday parties is miserable. Wheat is a tough allergy. Even though we don't eat much of it in our household, we're hoping our allergy elimination diet finds my son doesn't have trouble with wheat, because we'd like to be able to splurge on it here and there, such as at birthday parties and restaurants.