Vaginal vs. C-Section with narrow pelvis?

Hey ladies! I’m 37 weeks now and my baby girl is measuring at 6lbs 5oz and facing down! Yay!! Keeping the same due date (6-8) but she said we can induce in early June, iffff we wanted to. It’s hard because she knows I want to do it vaginally and she still thinks that’s a good option, but worries because my pelvis is very narrow that even if I get to a 10 with dilation, that I could need a c-section anyway. She hates me to do all that work on me and the baby, if there’s a good chance it wouldn’t be safe for Everly’s exit after all. There’s so many risks with c-section and I’m not sure what to do. She also said Everly looks good on the sonogram and that she'd be happy if I went into labor anytime!

Thoughts? Experiences? Recommendations?