I really don't envy you your dilemma! Your proposal sounds over-generous to me but it largly depends on the character of your 13 year old and whether she uses it continuously within those hours or fits in her other activities such as sport/homework as well.
There is so much that is good out there, but it is possible to stumble on the bad without meaning to and that can divert a 13 year old's attention.
Chat rooms can be a dreadful waste of time - but then I'm not 13!
Got a similar arrangement on ISDN at home here using third party software from NZ called Wingate and all Internet access is through the "Server" PC in my study. With it I can check on the URLs that my son has accessed when I've long been in bed and asleep.
I wish he spent as much time reading his orthopædics as he spends playing Backgammon with folks (usually Turkish) he has never met. But what can I say when he's 23?
You need to let your kid know that you are completely involved with her use of the Web and spend some time sitting with her, discussing where she's been and what she thinks.
Other than that, I wouldn't presume to tell anyone how to bring up their kids, so excuse me if I trod on your toes.