A lot of teachers advise their students to obtain the Tune A Day book or the Abracadabra book and structure their lessons working through these, and then the student still has the book as back up for homework, practice and reflection. Don't forget the Scales and Arpeggio's book too.
I agree that all good/great players are not necessarily the greatest teachers. Neither are all the greatest teachers so brilliant at performance themselves. In others words, being great at one does not necessarily mean that you are great at the other, neither does being crap at one mean you can't be great at the other.
Until you have a go at teaching someone else, how do you really know whether this is a skill you are good at?
Remember your own learning, and take yourself back to those basic, initial steps into the world of sax, and remember that's where your student is at right now, and grow them on from there. Don't be tempted to introduce them to too much at once in each lesson. Less is more for getting those strong foundations.
Be ready to explain the same thing in several different ways in order to achieve clarity and understanding for your student(s). Not everyone understands the same thing linguistically and may need a variety of explanations before the penny drops. It will serve to benefit yourself in increasing your own saxcabulary whilst also highlighting your areas of great knowledge which you may have been taking for granted, and may also open up a few gaps to go fill too (every student brings along some great lessons for the teacher too and sometimes that lesson is "how NOT to do things"

).
I wish you and your new student happy times/tunes.
Mel