Yes, child actors who earn income have to pay taxes like the rest of us. And possibly another 15% funneled into a Coogan account. What parents must do, whatever state they live in and however much money their kid does or does not make as a performer, is manage that money responsibly.
Did Steve Jobs leave his daughter any money?
Lisa Brennan-Jobs, now a 42 year old author and a Harvard graduate, had a different experience growing up with her father than her half-siblings. After his death, Steve Jobs did make sure to leave Lisa with a multi-million dollar inheritance.