I think that all of the safety precautions you take as a blogger would need to be doubled for your daughter. Personally, I don't have a problem with a teenager blogging, but she would have to follow rules (if she were my daughter):
No use of her real name
No reference to address/location
Personal life details left out
I would need access to it
There was a segment a year ago or so on our local news station. They showed how incredibly easy it is for predators to gain info on kids/teens via myspace/blogs. Even if the underage child was careful, there would always be enough "tells" to give the predator enough info to know daily activities, location, school, etc.
I think I would allow my child to have their own blog, probably on blogger, and set it up with limited public access, make it password protected, and discuss with him/her who they would like to invite to view the blog.
I would not encourage the social networking stuff for a 13 year old, but I'm pretty protective of that kind of thing.... it's a big, big internet out there..... But invite family members, a few school friends, and then I'd say go for it.
Or perhaps your child wants it as more of a personal journal and just wants to do a private, non-public blog..... Blogger has settings where you can make a blog private, invitation only, and where it doesn't appear on any searches.
I have a few blogs that are more family scrapbooks that no one has access to. I love recording photos online and being able to journal via the laptop.
I had started a blog for my two year old where she "talked" about her day. No pics. No videos. Just text. Well, someone started a blog mocking my daughter's posts. I quickly took her site down and it's not come back since.
Years later someone did the same to my blog. My husband says that's how you know you've made it as a blogger- when you have as many people hating you as adoring you. It's creepy to have it happen to an adult and frightening to have it happen to a child.
Let your teen know there are cruel people online and not everyone is going to leave nice comments. Let her know of the dangers, too. She needs to understand there is a dark side to blogging and her safety is the number one concern.
Then you monitor it like crazy. Watch the traffic. Make sure there aren't tons of hits coming from a prison or anything.
I know I sound paranoid but I've lived through some awful times as a result of my previous blogs. It showed me that people can be so kind, but they can also be cruel. And scary.
My children are 6 and 4 so they don't even know what a blog is but if they want to start their own when they are older I will definitely have it set on invitation only and I would read it everyday. It's scary what we as parents have to look out for these days.
My 10y/o loves to write too and has her own blog. HOWEVER, her blog is only open to the friends that we've invited, and I make her write under a pseudonym. I'm a co-author on her blog, so I can edit it as I see fit. Since she keeps "outting" herself and her friends I refuse to open her blog up for everyone to view. She just doesn't get that she needs to protect herself out there yet.
One of the main problems we have with this is that I have a friend (my DD is friends with her child) who doesn't feel the same about internet safety. She regularly uses her kids real names and pictures on her blog, and allows her child to do the same with an open blog. *sigh* So I constantly hear from my child "But BFF's mom lets her do it!" I have to regularly pull the "mean Mom" thing.