I liked your overall approach, the lesson plan was great with logical progression -
With adults, student interest is normally high, but with children it can and may vary considerably!
The average 'attention span' of any student on any topic is only about 20 minutes - beware of this!
I have followed many different variants of 'standard procedures' - some work - some do not - it depends on the student!
For a 'first time' student with absolutely no knowledge of a 'second language', I can suggest a method that works, and can bring them to a decent level of competence in ESL within about 6 months.
Initially aim at 'basic english'
Work with and encourage the student, but not intensively!
In their home (with your help) they should 'stick' little labels in English on everything in the house, with only verbs, articles and nouns - the rest can follow later.
What then happens after a short while is miraculous! - Try it!
Within a short time they will have accumulated quite a large vocabulary, and achieved a good level of competence!