Poached egg on toast
There are lots of great projects to do with eggs. You might start by just cooking an egg for yourself to eat. Do you know how to scramble an egg? Hard-boil an egg? Poach an egg? Learn a new way to make eggs at home.
Next, learn to make eggs the way people did in the ancient world. To roast an egg on a campfire, wait until the campfire is a bed of hot coals. Poke a small hole in each end of the egg (so it won't explode) and put it in the coals, and wait about ten minutes. It should be pretty much the same as a hard-boiled egg.
You could also try pickling eggs. To pickle an egg, first make a hard-boiled egg, peel the egg, and put it in a small glass jar. Then boil a cup of vinegar with some spices like ginger, allspice, or pepper for ten minutes, then take it off the heat. When the vinegar cools down, pour it over the egg and put the lid on the jar. Store the egg in a cool, dark cupboard for at least a month and then you can eat it. People used to pickle eggs a lot back when chickens only lay eggs in the summertime, so they could have some eggs in the winter too.
Finally, how about decorating your own Easter eggs?
Chicks & Chickens, by Gail Gibbons (2003). Explains where chickens come from, and what they eat, and so on. For younger kids.
A Chicken in Every Pot: Global Recipes for the World's Most Popular Bird, by Kate Heyhoe (2003). Includes a brief history, and lots of recipes for chicken.
Much Depends on Dinner: The Extraordinary History and Mythology, Allure and Obsessions, Perils and Taboos, of an Ordinary Meal, by Margaret Visser (1999). Background on what you eat, including a chapter on chicken.
Food in Antiquity: A Survey of the Diet of Early Peoples, by Don and Patricia Brothwell (1998). Pretty specialized, but the book tells you where foods came from, and how they got to other places, and what people ate in antiquity. Not just Europe, either!