Afraid of means having been caused to have (i.e. possessing) fear of. "Of" in this case means "resulting from," with the full implication that the entity feared is also the causative agent of the fear. In other words, if we say George is afraid of ghosts, then we are essentially saying that ghosts made George afraid of them.
Thus we can see that "brave of" would not be syntactically equivalent. Brave does not mean having been caused to have bravery. It means "bold; possessing courage; unafraid." This is not a result of the effect of any outside agency. A ghost cannot make George brave. So I find "brave of" to be grammatically invalid.
Alternatively, I have heard the usage "brave about," as in "George is rather brave about doing things most people wouldn't venture to do." And I believe "about" could be used in place of the "of" suggested in the OP; for example, I think you could say, "George is brave about ghosts," although generally I think people are more comfortable saying "brave about" an action, such as, "brave about going into a haunted house," or "brave about" some generalization, such as "brave about anything that has to do with ghosts." Another way of putting it would be "brave when it comes to searching for ghosts." These are just a few examples; there are more.