You can go up to 2 weeks past your due date and that is still considered term because of date errors. Induction has risks, so if you don't go on your due date, don't rush yourself. Membrane stripping isn't necessary either.
I think it's terrible that your doctor is being so invasive and trying to rush things. If you aren't ready, you aren't ready and she shouldn't mess with that. If you are more than a week past your due date, or the baby is getting too big, or there is a specific and real health concern, then go ahead with induction.
The only risk with waiting for labor is if the placenta starts to detach and disintegrate because it is only meant to last for a certain period of time. But there is no way you will be to be worrying about that at this point....there is still plenty of time!
Just give yourself time and tell your doc to have more respect for your body and your baby too!