Baby Costumes & Baby Halloween Costumes. You're never too young to celebrate your first Halloween. Pick out one of these adorable baby Halloween costumes to show your new baby's the sights and sounds of his or her first Halloween. Just be sure to get your little goblin back in time for bed. Your wee one can't miss out on the Halloween festivities. Commemorate their first with a baby Halloween costume that will leave trick or treaters gushing. So suit them up in these cute infant costumes.