Questions about Induction.

My doctor wants to induce me at 37 weeks and I’m currently 34 weeks today with my first baby, who is also my rainbow baby. She said it’s because my daughter isn’t gaining weight and she’s only in the 4th percentile but I’ve gotten huge the last few weeks and the specialist I saw last month told me she was in the 9th percentile and just a little small, as her dad and I both are small people as well. I wanted an all natural drug-free birth and I’m seriously upset about her wanting to induce me, I feel like it would make more sense to keep her in than take her out. What do I need to know and any tips anyone can give me? Any input is welcome!