I'm going to dump my girlfriend because of her unannounced backpacking trip.
Why would a backpacking trip be a reason to break up with her?
I can't trust her after this unannounced trip.
It can be upsetting when a loved one doesn't involve you in their hobbies and even worse when they plan something without asking for your input, but breaking up with them over it is a little bit harsh. You shouldn't break up with them just because they didn't tell you about one of their hobbies and instead you should tell them you want to be more involved in their life.
I don't care about all that. I'm breaking up with her.
I really think you should think about it a little more, because breaking up seems like an over-the-top reaction. I get why you're upset that she didn't talk to you about the trip, but I really think that it would be a mistake to break up. It might be better to talk to her about how you feel.