Thanks for all the replies. Just to clarify, I did say in my opening post that I'm very much in favour of teaching her to be responsible - and I should have said that the only computer she uses for the internet at the moment is in the kitchen - when she does use it, it's when a parent is cooking. You're all absolutely correct that teaching her not to give out information and so on is the best thing to do.
I think I was more thinking of protecting her from the many ways companies (and individuals, I suppose) might try to exploit her online rather than to stop her seeing things, to be honest. She has my old laptop but only uses it for offline stuff, and it's running Linux so it's pretty secure anyway I guess, compared to Windows at least.
The time thing isn't an issue at the moment because she never takes any device upstairs anyway. I used to work in schools, and also in IT, so I know kids tend to find ways around things - I was thinking of connecting the proxy directly to the router which in turn only provide internet access to it (filtered by MAC address or something) and securing those settings via password, but I suppose she could if she wanted just put a clean install on the proxy because she'd have physical access to it (because it'd be behind the tv next to the router) - I would imagine that when it got to that stage I'd accept that she knew what she was doing

(And as I typed that it occurred to me that she could get a PAYG data dongle when she's older anyway)