Check all of the ACL entries. There is a check-box for every entry labeled "Replicate or copy documents". If it is not checked for the entry that applies to you, then you are not going to be allowed to replicate. Also, note that there is a very serious side-effect from this setting, which is described in this IBM technote. Even if you check the box for the ACL entry, you will still be prevented from replicating any document that was previoulsy created or edited by you or any other user who did not have the "Replicate or copy documents" permission. (I consider this a design flaw in Domino, but IBM apparently disagrees.)
BTW: Anonymous access would not apply to you with the Notes client. (Well, actually there are cases where it could, but it's unlikely this is one of them. It applies only to public Domino servers that allow unauthenticated client connections, which are very rare.)