id personally just stop her from deleting the history. if something worrying shows up there then thats when you should take action.
if your child is sensible then give them a bit of trust. chances are they will obide by your rules, and if they dont then you should monitor them all the time. i respect my parents and their rules far more when they respect me back/trust me on things.
just remember that proxies are out there, and she could discover how to use them, and its very hard to block them all.
its a dark and dangerous place on the internet, but if she really really wanted to look at something, then im sure she would find a way to do it no matter what you did anyway (a friends house maybe, etc).
if you feel you can trust her then please do so. even if she is only 12 theres no need to treat her like a baby. just see how it goes.
ultra vnc is a good program if you did want to try. besides, its always good having that program on all your computers if you need to view/control them for any reason