When writing becomes automatic enough that they want to write their stories down.
At your daughter's age, I was the same way - told lots of stories but refused to write them down. The reason was simply because writing still took a lot of effort, so much that I couldn't get the creative juices flowing while trying to write things down. At six, your daughter has probably just barely started to read and write. It still takes her full attention to do it.
By grade 3, schools shift from expecting kids to 'learn to read' to expecting them to 'read to learn', because at this point, most kids are good enough at automatic reading that they can absorb a new concept by reading about it. Even then, writing still takes more effort, because an 8 year old's fine motor coordination isn't that good yet.
In my case, I started writing my stories down around 11 or 12. Before then, writing was just too much effort. Now, as an adult, I've written (but unfortunately haven't managed to get published) several books, and I often write for fun.
If you want your kid's stories to get written down before that age, maybe try dictation. She tells you the story and you write it. You can read it back to her, or ask her to read it (but don't push - you don't want a creative activity to be linked in her mind with effort and pressure).