With the exception of the domain name. But does a little girl making her first website really need her own domain? Especially if you aren’t sharing it with people she actually knows?
As for a Facebook clone for kids: I’d look at kid’s websites, like neopets.com or clubpenguins.com. Sure, they have a game thrown in there, and have less options, but they also have more kids who would actually see your daughter’s work and comment on it. And yet they’re moderated, so it won’t be mean.