Advice on teaching Go to a kid
My recommendation is to:


Introduce recording of the games. This would allow her to study her own games offline, and come back with questions. The habit of recording one's own games is a gift beyond price, and the sooner introduced the stronger the habit will be.
Ask this young girl her own opinion on these questions. A sense of control I believe is vital, and she may well have different choices each meeting. In presenting these choices try to describe them in purely factual terms - just the data without any bias you may have. For the 13x13 board, describe how the balance between corner-play and centre-play will change for example, and ask her when she thinks she is ready for that. Avoid presenting it as a "promotion", so there is no shame in going backwards. Just present it as two different variations that will practice different skills.
In regards tsumego, I would introduce the various types of study, joseki and others, and show her that these are specialty skills that can be practiced and studied on their own. Then let her choose.


I was just two yeas older when I learned chess. Every Thursday evening at 7:00 my dad and I would setup the board under his favourite chair, and I would lose. I bought a book on Openings and another on Combinations and studied those  during the week. I found a couple of friends to play against as well. Eight months in I got my first draw against my Dad, and a couple of weeks later my first win. One of my fondest memories.