The use of "I don't have" now is what we once used "I have not" for. But now "I have not" sounds pedantic or old-fashioned. For example, people would say, "I have not a minute to spare." Today, we say, "I don't have a minute to spare." Before, when asked, "Do you have the time?" we might respond, "I have not the time, sorry." Today, when asked the same question, we respond, "I don't have the time, sorry." Technically, they would have asked, "Have you the time?" The helping verb (or auxiliary verb 'do') is now used when before it wasn't. So, in tag questions, you will now see this: "You don't have a brother, do you?" Before you would have seen this: "You have not a brother, have you?" Today, you will see "have not" as a response to a comment or question using the perfect tense. For example: "Have you finished your homework?" Answer: "No, I have not." So, 'have not' is still used today, but it's used as a helping verb response or tag question, not as a verb (unless it's purposefully antiquated speech: "I have not time for your tomfoolery, good sir!"