This is a difficult one. I'm assuming that you bring this up because you've both been part of discussions of a sensitive or personal nature. I agree that for now, it's probably best to just pretend that it isn't her.
However, as others have suggested, it might be wise to let her know about this if you think you'll be seeing more of her. Depending on the nature of her personal revelations on the other board, it might also be a kindness to clue her in that it's not as anonymous as she might think.