Royal Commission on Child Abuse - Is a petition to the Queen appropriate?

According to this document, PETITIONS TO THE QUEEN every subject of the Queen has a right to petition her.

I've written previously about the mess that the Home Office is making of the Child Abuse Inquiry for England and Wales, for example  The Inquiry Panel and Keith Vaz must go - Letter to Theresa May and Mark Sedwill

A legal challenge to the Home Office-sponsored England and Wales Child Abuse Inquiry has been launched. It is not yet clear, so far as I'm aware, whether the High Court will give permission for Judicial Review.

The issues in designing a fit-for-purpose Child Abuse Inquiry are complex. See, for example, Scratchpad - Designing a once-in-a-lifetime Child Abuse Inquiry

One issue I see as particularly important is ensuring that cross-border connections are not missed. To that end I think it is crucial that information from Northern Ireland and from Jersey are collated with information from England, Wales and Scotland.

One possible solution is a Royal Commission on Child Abuse.

The geographical scope of such a Royal Commission on Child Abuse would include Jersey (and possibly other Crown Dependencies).

No UK Government inquiry can formally include Jersey since Jersey is not part of the United Kingdom.

However, since Jersey is a Crown Dependency, it seems to me that a Royal Commission on Child Abuse could include Jersey (and, if appropriate, other Crown Dependencies) in its scope.

Is a petition to the Queen an appropriate vehicle to use to put consideration of such a Royal Commission on Child Abuse officially on the agenda?

It's a question to which I'm giving serious thought.