how they could control what their daughter did on the computer
They really don't understand do they?

A 9 year old girl is not going surfing pr0n............ so it is not controlling what their daughter does on the net, it is more a case of what the net might do to their daughter. There is one hell of a difference there!!!!

The first thing IMO is family trust...........warn her of the dangers of "clicky, clicky", the nine year old is a 45 year old pervert and so on.

You really ought to be looking at defence mechanisms rather than restrictive ones IMO