I understood the sentence in another context. Let's imagine your father helps you to take care of your child during about one month. Then, one of your friend asks you about your father:
- 'Quante settimane ha il tuo bambino?' / 'How many weeks does he have your child?'
Could it be a correct sentence in that context?
Hm no, in that case it would be "Per quante settimane ha il tuo bambino?" (For how many weeks does he have your child?). This sentence has two readings, one asking for the child's age, and one asking how long the child has left (to live?) :)