The time to think about getting an agent is when you hear from professionals that your child actor is competitive and marketable in the industry. That will come when your child has been getting callbacks for jobs and has been working. She’s been hearing feedback on her performance and skills. Then you’ll know that you’re ready to look for a manager.
There are plenty of opportunities for young performers who don’t have agents. Almost all theatre and musical theatre jobs are cast from open calls that are available to everyone. It’s true that more opportunities are open to child actors who have representation. But it’s not true that a performer cannot find work without an agent.
Casting directors don’t limit their search for talent to child performers who have agents. They are really only interested in whether your child can do the job.
What’s most important in your child’s success is not to start looking for an agent or manager until your child is ready for that next step.