The Simple Present of the verb to have is slightly irregular, since the bare infinitive is have, whereas the form of the verb used in the third person singular is has. (she has, he has, it has)
do , does (for the third person singular) are auxiliaries to form questions and negative statements in the Simple Present.
When the auxiliaries do, does are combined with another verb, the other verb always has the form of the bare infinitive.
So, she doesn't have a book.