ASPCA officially recommends dogs and puppies for children over 6, since the majority of dog bites with children are under this age. 

Most important thing is that an adult must carefully supervise both child and pet.  Especially at the beginning when a pet is introduced in a family, or when a child is born into a family with pets, supervision is the key to teach appropriate behavior.   It is imperative for the child’s safety to teach appropriate ways of touching a pet.   It is also important to observe the pet, to enforce positive behavior through reward and praise and correct inappropriate behavior consistently and kindly. 

A kitten that is treated softly and kindly by people will be more sociable when older.   A child who touches a kitten roughly and chases or follows it when it wants to get away, will teach the cat to dislike humans and be aloof as an adult. Similarly, a dog who is treated kindly by all members of his family will be a safer and friendlier dog.  Many dogs, especially small ones, living with children that pull their tail or touch them roughly exhibit nasty and dangerous behavior especially to children.