Technically it would be a W-4 not a W-9 but for the same reasons ... to get the employee's name, address and SS# since a W-2 needs to be issued at the end of the year. The child & company is not required to pay FICA taxes or even fed/state withholdings but quarterly payroll tax forms do need to be timely filed.
https://www.nolo.com/legal-encyclopedia/why-its-tax-smart-hire-your-children.html#:~:text=Hiring%20Y....
