Before answering the question of whether you SHOULD, I'll say with almost complete certainty that you are going to. It's right there in the way you tacked on a flimsy justification at the end of your question. You might as well have ended with "also I'm pretty sure she drowned a sack of kittens."
You are justifying this decision, which you have already made, to yourself. Both by coming up with reasons why it's okay to date this guy, and by asking me, hoping I'll say go for it. And you know what?
Go for it.
Because honestly, a year is a long time, and people need to move on. Breaking up with someone is admitting that you no longer have responsibility for that person, can demand nothing of them, and don't have to remember their birthday anymore. If you can't handle that, you shouldn't break up.
Which isn't to say this won't ruin your friendship with said girl. The fact you felt moved to ask the question implies she might be a bit of a drama queen, or possessive of her exes. If that's true, my official sanction isn't going to keep her from showing up at your house at three in the morning to claw your face off.
So sure, it may cause fallout, but yeah, go for it. You clearly want to, you're probably in the right, and your life will be richer for the experience however it turns out. Unless she cuts your brake lines, that is.