Homemade Fake Egg: Use the following recipe in place of one egg in baked goods; it works really well in cookies. It's best to whip it up right before adding it to the recipe. (Note: This recipe is not meant to replace eggs in really eggy dishes, like scrambled eggs.)
1 teaspoon baking powder
1/2 teaspoon baking soda
2 Tablespoons flour
3 Tablespoons water
Combine ingredients in a small bowl and mix together with a fork or wire whisk until foamy.
Eggless baking can sometimes be a daring adventure, but that doesn't mean you shouldn't experiment. If you end up with hockey pucks instead of cookies, don't worry. Try something different next time.