Even if they counter, do you really want it? Take the new job unless there's a great reason not to.
The new role I just accepted skyrocketed my wages past my old boss (Manager), his boss (Sr. Manager), his boss (Director), and her boss (VP). Only person at the old plant that had wages approaching the new job is the CEO. Easy decision, aside from the part where I really believed in what the old company was doing, even if it was killing me.
Once you announce that you have an offer, it changes things. If nothing else, ride off into the sunset for a couple years and come back later with more experience and a broader understanding of the world. And a record of higher pay. It's better to leave and come back than stay with a counter and have people wonder when the next time you'll interview to up you salary will be.