In my opinion kids just shouldn't be on the internet at all until they are old enough. They could be introduced for education purposes under strict supervision from an early age, but apart from that, why would anybody give their child free reign of a global network.

Television does enough damage to creativity and imagination without video games and youtube videos as well.

As for terrorism... You can shut down the internet, shut your doors and stay inside for months, that won't stop them. Life just has to go on.