What is the ruling on the traditional prostration performed in Pakistan to celebrate a daughter reaching 40 days of age, and is there any basis for it in the Sunnah of the Prophet?

There is no basis for the prostration of gratitude (sujud ash-shukr) performed by the questioner in the mosque forty days after his daughter's birth. Prostration of gratitude is legislated immediately upon the attainment of a blessing or the warding off of an affliction. It becomes void with the passage of time, and what the questioner did is an innovation (bid'ah).