A baby gecko will eat the same type of diet as the adults but in smaller portions and smaller feeders. A baby gecko will require feedings daily. They can eat pinhead crickets, wingless fruitflys or small roaches depending on size of the animal.
Normallly, the baby house geckos will eat insects such as gnats, and yes they can catch them, and baby crickets, i think they might eat some kind of plant, but i am not sure. do some research before keeping ahouse gecko.