The dream journal on here has a private entry function if there is a dream you really don't want to share. However, your first post must be public. After that, you can have all your dreams as private entries if you like.
I keep two journals, a handwritten one, and the one on here, which is a typed version of the handwritten one.
If i have a dream i don't want made public, i either make it a private entry, or don't put it in at all. No one else is any the wiser.