What happened after the devout lady from Berhampur dreamt of Baba? Did she and her husband go to Shirdi?

Indeed they did. Following the dream where Baba asked for khichdi, the lady and her husband became very eager to have Sai's darshan. According to Chapter 28, her husband, an officer in the Post Department, was later transferred to Akola. From there, the devout couple planned their journey. They chose an auspicious day and set out for Shirdi, even stopping to worship at the Gomati tirtha en route. Upon their arrival, they lovingly took Baba's darshan and served His feet daily, staying in Shirdi for two months with joyful hearts, happy and fulfilled in their devotion as Chapter 28 narrates.