Unless you drive erratically or give the police any reason to stop you, there's a high chance that you won't get pulled over while you're on your road trip. But, ultimately, you never know what's going to happen - so it's still a good idea to have your paperwork to hand. You should make sure that your driving license and registration are readily available, and easy to find if you do get pulled over.
In most cases, the easiest place to store these items is in the glove box or the center console. Just make sure that you ask the officer for permission to retrieve them before reaching in there.