After much pestering I agreed to set up a trial account for DD that I could monitor, with just a couple of friends as contacts. I'm horrified by what I see and am regretting it already.
There is a '13' age limit for a reason. I even wonder if it should be 16 like whatsap. One of the few friends DD is testing this out with has a public account linked to a load of strangers, because apparently it is 'cool' to acquire as many followers as possible. Some are companies pushing their products; many appear to be older (male and female) teenagers who swear a lot. I don't see it to be appropriate for an 11 year old to see inappropriate material posted by teenagers, e.g. referencing self-harm, anorexia, guns/violence, nudity, drugs, etc. - and I saw examples after checking just three or four 'followers'/'following'. Then there may be others who are targeting the web to make contact with children... While most other children may have set their posts to private, if they comment on a public post their username and comment can also be seen by everyone. The only way round this is to make sure (a) you are 100% sure you know who you are linked to and (b) you do not follow or are not followed by anyone who has a public account. You can test that by googling their username but I doubt children will be rigorous about this.
But then, profile and biography details are all public ieven if posts are private. I'm literally shocked by the number of children who have not only uploaded a picture of themselves to their profile - sometimes in school uniform! - but have included their full name, form group(!), names of friends, school and where they live.
To be honest, there's also a danger even if you're not on Instagram of your friend mentioning your child's name, the fact that she goes to the same school she's mentioned in her profile, where they'll all be at 3pm on Saturday. The biggest danger really is other people's children.