Will the deceased child intercede for her parents and supplicate for them?

A child can intercede for their parents. There are hadiths indicating the virtue of one whose child has passed away, and that they will enter Paradise because of the child and their intercession, such as the hadith: "There is no Muslim for whom three children die before reaching the age of puberty but that they will be met from the eight gates of Paradise, from whichever one they wish to enter," and the hadith: "Their little ones are the 'da'amees' (little creatures) of Paradise. One of them will meet his father and take hold of his garment, and he will not let go until Allah admits him and his father into Paradise," and the hadith: "There are no two Muslims between whom three children die before reaching the age of puberty but that Allah will admit them into Paradise by virtue of His mercy upon them. It will be said to them: 'Enter Paradise,' and they will say: 'Not until our parents enter.' So it will be said: 'Enter Paradise, you and your parents.'"