Trying to decide whether or not to get an induction

Please keep this judged free.

My doctor has delivered all four of my babies. Hes the only one I trust. I had a bad experience with a doctor when I was 16 and their neglect caused me to have a stillbirth. This doctor is amazing and have delivered me 4 healthy babies and I really want him to deliver baby #5. So here's the deal. If I don't go into labor by next Monday(I'll be 40 weeks 2 days) he won't be able to deliver my baby because he's going on paternity leave for an adoption. He said if I want he can induce me this week, and of not the other doctor will take care of me. I have so much anxiety and I can't imagine having another doctor deliver my last baby that isn't him. Plus I have heard very bad things about this other doctor from friends who have had her. The whole thing is giving me so much anxiety...