This question is not easily answered because it depends on the child. Some teenagers are not aware of the responsibilities of pet ownership, while there are many very responsible 7, 8 or 9 year olds who understand the commitments required. You will have to make your own assessment as to whether your child is ready for the responsibility of a pet.
If you decide that your child is ready enough for the responsibilities of pet ownership, perhaps you should start with an animal which is easy to care for. You can find this out by searching through resources such as reputable books and internet sites, and by speaking to your vet or local RSPCA shelter. When choosing a pet you must also consider what kind of animal would best suit your circumstances. Remember also to factor in your lifestyle, housing situation and the cost of owning a pet.
Adult supervision may be required, even when the primary care of the animal is granted to your child. If your child is responsible for looking after a household pet, make sure that the animal is appropriately housed and fed, and is receiving veterinary care where necessary.