Put yourself in her shoes. You wouldn't her to look into your account for any reasons ... it's an invasion of privacy. Now this is a trust issue. Who do you not trust? Yourself or her? Do you think she isn't trust worthy after you have gotten to know her? Or did you make the wrong decision in starting a relationship with this person? You're going to have to put more trust in either, your decisions of who you choose to be with, or believe in the person that you are with. Now there is a difference in thinking if you made the wrong choice or if she turns out to be the wrong choice for you.
But you are never going to know unless you talk to her about it and trust in her. But usually in a relationship, I'd give it a little bit of time to see if she starts acting different after you talk about whatever is bothering you. Like, ignoring you or paying a lot less attention to you and disregarding your feelings. Then I would just assume that she is not the one and make my decision that way. But if you start acting different w/out talking to her, then she will know if something is up.
First of all YES IT WOULD BE WRONG!!!!!!! Haven't you ever heard of trust? I mean if she is your girlfriend you should trust her.....unless you have a reason not to. No matter what though don't hack into her account.....she could find out (cuz girls are smart like that) and she would most likely break up with you. With no trust there is no relationship.