AnswerA. Fish, as long as it's mashed up, is safe for babies who are 6 months and older. Choose swimmers that are low in mercury, such as salmon or mahi mahi. Waiting to introduce foods usually associated with allergies (fish, shellfish, cow's milk, eggs, peanuts, nuts, wheat, and soy) does nothing to prevent allergies, according to the American Academy of Pediatrics. But do avoid choking hazards like grapes, hot dogs, popcorn and raw carrots.