When should my child...? Is my child ready to...? I'd like my child to work on... 

Those are some common lead-ins to the ultimate idea of: "My kid is pretty young (6-9 years old) and I am seeing a need for some formalized performance training. Am I crazy? Can you do this? Is it safe?" Are sometimes the follow-ups.

Yes, children in that age range can absolutely start a structured performance training plan. It is safe. However, unless your child has a real need or is super motivated for structured training, I would encourage you to try gymnastics, parkour, or other sports before committing to a performance plan.

What and who should you look for?

Look for a facility that specializes in training for children under age 10 or 11. And look for staff members and coaches who have lots of experience working with young children. 

Look for a big emphasis on fun, guided discovery, and inquire about how the structure changes from age 6 up to age 10 or so.

Generally, females aged 7-8 are ready to start as they have the mental focus and body control for a full training session. For boys, usually it's age 8-9 when they are ready.

The sessions do not need to be a full hour - probably around 45-min is ideal. Because this is not a sport with breaks for talking about strategy and technique, the sessions can be very tiring because they are so focused.

Here is a sample template that can be used for any young child (scaled appropriately):

With some common sense applied to these sessions (mostly remembering the trainee is a very young child), they will be fun and productive for everyone.