Unfortunately not. You can't have text messages automatically forwarded off the phone. The only way to view the content of the message is on the device directly.
Take her phone and read the messages if you're worried about them being inappropriate! My parents did it to me all the time. If she has nothing to hide, she won't have a fit about it. If she starts freaking out then you'll know she's being a bad kid. You pay for the phone, you're the parent. Take charge!