It mainly depends on what she wants to do. And her skill set.
DD had West End contracts as a child and loved it. Most of her close friends were in West End. It's a big juggling act for parents and you really need to be within M25 to make it work.
She trained in acting/singing/dance for years. Singing was always her first love, acting second and then dance.
She is aiming for a career in the music industry and switch at 12 to focus on instruments and composition, and dropped the dance. But has 9 years of ballet, modern and other dance genres behind her. Still dances but not in a serious way - enough to keep fitness and basics up.
She's still very serious about acting - but screen not stage - but with that it's far harder to find or make opportunities.
If you are aiming for child roles in musicals, it is extremely competitive, these kids train hard, and you have to be very realistic about things like height. Matilda is generally 9.5 - 11 years old and UNDER 4ft 3". If your child is tall for age, or likely to develop early then they will struggle... there are hundreds of teeny kids out there. You are also finished at 13 or 4ft 10"/5ft - whichever comes first.
For MT, there are normally open calls, but on the whole you would want to get an agent involved. Look at the AYPA for reputable agencies.
For all those who say to come back when they're older... you can, but there are plenty of children who do know what they want. I know kids who did 4 or 5 west end shows and have now taken a different path, know lots of did 4 or 5 and are now in adult roles.
DD told me what she wanted to be when she was 3... she has never waivered from that and still wants the same thing. And it was not a world I had any knowledge or desire for her to be in. I've been on a very big learning curve. She knows she can always change her mind at any time.