I asked my indonesian husband about whether this is supposed to mean a one off "experience" or "experience" gained over time. He said it was the latter. So it doesn't make sense to use "the".
"She does not have experience writing books." Would probably be better.
She does not have the experience to write a book.
This extends the idea of having experience of writing books, to the experience needed (of a subject) to write a book.
Is this written differently in Indonesian -- why is my translation not correct?