still no baby

China
I am 39 weeks measuring 41 weeks. Yesterday I found out that I will be having a big baby. She's weighing  9 lbs and the doctor said ultrasounds are sometimes off and she will either be 10 lbs or 8 lbs they are hoping she's 8 lbs. I am starting to worry that my doctor will want to induce me or that she will suggest a csection. I am planning to do everything naturally and been planning a home birth since I found out I was pregnant. What are the chances my doctor will recommend we go with an induction and/or csection? I've had lots of false labor and it's frustrating me cause everytime I think something will happen the pain doesn't worsen , I know baby will come when she's ready but I really hope soon. 😐