Inducing at 40+2

I always swore up and down I would never get induced and let my baby cook for as long as they needed to. At my 39+4 appointment today my doctor asked about inducing. She said she wouldn’t let me go past 41 weeks but I could induce before and 40+2 would be a good day for her schedule wise. My husband got super excited and said we should do it. I didn’t feel pressured to agree per se but I got caught up in the excitement I guess. Now that I’m home I’m afraid it’s the wrong choice. I’ve read all these horror stories about inductions gone wrong and needing c sections by the end. (I want to deliver vaginally) On the other hand I read the longer they stay in past their due date the higher the risk for still birth becomes. I don’t know what to do. 😱 Is inducing at 40+2 weeks on a completely healthy pregnancy silly to do?

I know there is a chance I could have the baby before then but I feel like it’s not going to happen since my doctor said I’m barely a finger tip dilated at this point. FTM here if you couldn’t tell.

I want to add I trust my doctor completely and if she tells me I need a c section I will absolutely get one. My question isn’t about what I should do once I’m already in labor, it’s about making the decision on how to go in to labor.