Traveling with new baby?

So my LO is due July 3rd. My mom will be coming up to CT to help with my other two boys for about a week when I deliver. But recently, she’s started asking when I’m bringing the baby down to visit everyone else, including my InLaws, in VA. She wants us to come down before summer ends since both my boys start school in September. That would mean driving 7 hours or more with a baby that is around a month old. That seems to early to me but my mom and my husband both think it wouldn’t be too bad. I do want to go down and show all of our families our baby but I don’t know if summer is too soon? Any advice or tips would be appreciated. TIA 🙏🏻❤️