Hey that is terrific the way she reads to her dad.

I tried to encourage my dd to write when she was 6. She would write shopping lists without a fuss (even if just one or two items) but not anything that seemed like writing practice. Though I agree with the pp that if you had her tell you something and you wrote it down and asked her to copy it or trace it, that might seem interesting.
DD is 7 now, still gets some letters backwards on ocassion, but I see it reducing and think that will correct itself pretty soon. Just to make sure she didn't forget how to write the letters we would play hangman and secret coded message games, make labels for things - even if she is just writing a few words at a time, it keeps her in practice. Her handwriting has slowly and steadily improved as well.
She also makes greeting cards, which generally involves a bit of writing - at least the to and from names and a happy birthday. We also got into the habit of putting name and date on things.
In short - she will write if there is a purpose, and we had to be creative and resourceful to come up with real things that involved writing. e.g., I try to plan shopping trips well ahead of time so that she can make the shopping list. I also make an effort to write more on paper and not always on computer.
We keep a diary - she dictates and I write. now she has started doing a bit more of the writing.
We also started getting pen pals and that has motivated her as well. Last night she stunned me by spotaneously grabbing a sheet of paper and writing a full page letter to one of her pen pals, only asking me for spellings.