Here's why:
* "Has" is the correct verb to use when asking a question about possession in the present tense.
* "Have" is used for plural subjects or with "I" and "you."
* "A pet dog" is the correct phrase to use when referring to a single dog that is a pet.
The sentence "Does she has a pet dog" is incorrect because it uses both "does" and "has," which are both forms of the verb "to have" but are used in different contexts.