You need to get totally past the Introduction elements of piano study - through the Preparatory-Primary-Early Elementary-Elementary stages as your first goal of what to teach this child. Not all at once, but in continuous lessons. I do not think every other week works for children because if a mistake gets entered into her practice, she will practice that mistake into habit. She needs frequent input from you. Her attention span is going to be 30 minutes or less for each lesson at the keyboard in the beginning. Her back will get tired if she is spending too long on the bench, you will see her go into a "slump".
Because of her age and size, I would wait until she had hands together playing experience and was totally comfortable with herself at the piano making music before adding the scales and theory.
Acquaint her with a 5 Finger Position at Middle C, and then Parallel C (planting a seed for later bloom). With a very small hand span and fingers not yet strong and shaped, she can not physically get the results you want for her to have.
I use music with keyboard graphics to establish hand positions. This is secure and very helpful visually when all keys look alike to young students.
The theory, also not yet. Get her playing and relating musically to the piano first. Give her some good musical experiences first.
You can be collecting things you want for her to do under your guidance, but be cautious for when you choose to enter into them. You want for her experiences to be successful and happy making.
What I have said here does not apply to all beginners, my "ideas" are applicable for a new, 5 year old, transfer student, at beginning level. I would verify all of her previous pieces, and have fun having her show me what she can do. I would not start by correcting her, I would say let's do this again soon, and just use the input to get information about what she needs to be doing at this time.
Why don't you go to the different websites of music method publishers and see what is going on in the music they publish at this level. You may need to make a trip to a music store in order to preview where the methods take you over several books and into the future.
I stopped using method books about 10 years into my teaching and produced my own syllabus and pedagogy structure for teaching the different levels of music to beginners (very important level), intermediate, and advanced levels. It's been a lot of work to do this, but I've had lots of years to develop it.
I saw a new site in a music teaching magazine yesterday, I haven't been there yet, but perhaps it's something you will be interested in for the future: pedagogy articles, questions answered, teaching ideas exchanged. www.intermediatePiano.com
Also, Google: Martha Beth Lewis. This one is the surprize of your life and may take years to get through!
Let your student help establish her pace by having successful experiences.
Let's keep chatting here! The subject you are asking about is vast.