The auxiliary verb-full verb distinction is important. However the distinction between light verbs and full verbs must also be observed.
Consider your question, i.e.,
Positive statement: I do. Question statement: Do I? or Do I
In question statement which is the correct form?
In order to answer this correctly it is critical to distinguish between light and full verbs.
Light verbs cannot be used in exactly the same way as full verbs.
The form *Do I do? is incorrect because your verb, do, is not capable of bearing the meaning of the predicate by itself.
You must either use the first question—the tag question—or a fuller form of the second question.
The first form implies the full question by omitting it—forcing the reader to supply it entirely.
Do I do that work?
Again the change is required by the use of a light verb with a noun (do work).
You can avoid this by using a full verb.
Do I walk?