When you add any employee you get to choose which taxes they are subject to. I admit my experience with payroll is strictly the desktop version but in desktop if you do not specifically add taxes to each employee then none are taken out. For Online there at least must be a screen where you can view an employee's taxes and delete or override
But, just because you can treat your working children as exempt, should you? It is never too early to introduce them to the real world reality of take-home pay compared to gross earnings. It is never too early for them to start paying into the fund you intend to collect from yourself in so many years. You get a tax deduction for your employer share of their FICA