Advise first baby

Hi mummies, i had done my check as i am 39 weeks 2 days pregg till now my cervix doesn't open.done alot walking n exercise. I have always have this regular pain on my abdomen area hard as baby head already down. Can't hold the weight arching my whole body. Doctor mention it can hold till 41 weeks which i can't afford to hold any longer.😔 my Meternity leave start 4 December. Is it advisable to ask for induce at 39-40weeks if my cervix doesn't open? Any risk? #firstbaby #advicepls #1stimemom