Disappointed

I'm 38w+2d. Weekly doctor appointment is the same as last week, fingertip dilated, 50% effaced. Due date is June 4. However, doctor will be out of town June 5-18 so if he is overdue, some strange doctor will deliver my baby 😐 So now I have the option of being induced next week. I really wanted my first birth experience to be natural, you know where the water breaks or contractions start but that doesn't seem possible. Anybody else in the same boat?