Pretty horrible, in my opinion. It's not only disrespectful and a violation of her privacy, but it's a sign that you don't fully trust her. I think a relationship is pretty much broken if you have to resort to snooping to get answers.
But you don't seem to even be considering breaking up with her, so come clean about reading her journal, apologize, tell her what you learned, sit back and take it as she gets really angry at you (she's likely going to blame you somehow for cheating, have fun with that) and then you can suggest couples counseling.