Dame Rachel said the bill should introduce a register of all children being educated at home, which does not currently exist.
She added that there should be greater data sharing between health and education services as well as between different areas of the country to make sure children at risk can be identified.
She also called for an end to an exemption in assault laws that allows for the "reasonable chastisement" of children.
Surrey County Council has said that, now the trial has concluded, an independent safeguarding review of the case will take place.
Rachael Wardell, Executive Director for Children, said: "We are resolute in our commitment to protecting children, and we are determined to play a full and active part in the forthcoming review alongside partner agencies, to thoroughly understand the wider circumstances surrounding Sara's tragic death."