Doctor wants to induce me at 40 weeks

I have had a pretty healthy pregnancy although I have been in a lot of pain and have lot of trouble doing even the simplest  things without assistance. I pretty much expected that by me being very petite. I'm 5ft even. And this is my first baby and he is very large (more to love)... My doctor does not want me to go past 40 weeks.. So she wants to induce me. My cervix is not dialating so I'm doing everything I can to get things going so he can come on his own.. I really want to avoid being induced and a c section.. Trying not to get discouraged. But my mom kind of put a little doubt in my head when told me about her birth story with me and my sister.. She had to be induced with both of us and had to have a c section because she was not dialating at all.. The doctors told her it was because she was so petite.. She is 4"9... I'm just lost on what to do.. I'm trying to give baby as much time as he needs to come..