How can my 10 year old daughter start her career as a writer?
Short answer
She already has.
Long answer
The moment she puts words down because something inside her needs to, she has begun. Career is just the word adults use for what children do naturally: make sense of the world through story.
The most useful thing at ten is not craft books or writing classes. It is reading voraciously and writing without anyone grading it. A private notebook, no audience, no feedback. Just the habit of reaching for words when something moves her.
The writers who go the distance are rarely the ones who started with ambition. They started with obsession. Help her find what she cannot stop thinking about. That is her real subject. Everything else follows from there.