Doctor wants to induce at 39 weeks...

Hello everyone! I'm a FTM and currently 35 weeks 1 day. I had an appointment yesterday and had my first cervical check and my doctor told me I'm 1 cm dilated. I am due July 12th, but she suggested inducing me on July 7th at 39 weeks 2 days. I've had a great, normal pregnancy with no complications. I know it's only 5 days before my due date, but I'm really nervous/scared. I've heard being induced can be hard and stressful for me and the baby and can result in an emergency c-section. Has anyone else been through this?