One can NEVER play it too safe.

(Image from site)

Is it safe for kids?
"Instagram is not for children under the age of 13, and in my opinion, not suitable for slightly older teens, either. If you’re 12 years old, there isn’t even a 1999 year to choose when signing up. Instagram has strict Terms of Use and Community Guidelines that make their age requirement clear. Also, there’s an obvious connection between Instagram and other adult-intended social networks like Facebook and Twitter." (Mary Kay, 8 February 2013) - See more on her blog for parents called 'Helping Families Live Healthy Digital Lives' here
How to delete pictures and videos off an Instagram profile

How to delete an Instagram account
(Note: This can only be done on the website and not within the app)
As a parent/guardian you can contact Instagram directly to report a minor and request that all your child's/children's data be removed from their server as they are under age. Details regarding this with contact details are below under Children's Privacy.

What does Instagram have to say?
Instgram says the following about users younger than 13:

Terms and Conditions of Use has the clause under Basic Terms

Basic Terms

  1. You must be at least 13 years old to use the Service.

Instagram does not knowingly collect or solicit any information from anyone under the age of 13 or knowingly allow such persons to register for the Service. The Service and its content are not directed at children under the age of 13. In the event that we learn that we have collected personal information from a child under age 13 without parental consent, we will delete that information as quickly as possible. If you believe that we might have any information from or about a child under 13, please contact us.

View their user policy here