Place the eggs in a saucepan and cover with cold water. Bring to a boil, cover, remove from the heat, and let stand for 10 to 12 minutes. Transfer to ice water to cool, then peel.
Cut a very thin slice from the bottom of each egg so it stands upright. Cut off the top third of each egg in a small zigzag pattern, keeping each top paired with its base.
Gently remove the yolks and place them in a medium bowl. Mash thoroughly with a fork.
Add the mayonnaise, Dijon mustard, garlic powder, and salt. Mix until smooth, then transfer the filling to a piping bag or zip-top bag with one corner snipped.
Pipe the yolk filling generously into the egg-white bases. Position the matching egg-white tops slightly tilted over the filling.
Cut tiny triangles from the carrot rounds for beaks. Use a clean plastic straw or knife to cut tiny olive circles for eyes. Add two olive eyes and one carrot beak to each chick.
Refrigerate until ready to serve and keep chilled.