Question for the mommys

My little boy is a month old and is always hungry. He nurses constantly during the day and wakes up at night a lot to eat. His grandma (significant others mom) told me that it would help him be more satisfied to add a little cereal to his bottle. Is he too young for that? Have any of you mommy's gave cereal that early? I'm a first time mom, and don't know if I should or not.