The problem with a question like yours is that, really, no one can give you a yes or no answer. It might help; it might not; it might make things worse. Those are your answers.

Let me encourage you by telling you that in all likelihood your rifle will group better than the 1" you want just as it is. First of all, you realize, of course, that a different load might exceed your expectations without changing anything else. You are new to centerfire rifle, so you might benefit by having an experienced shooter watch you and coach a bit, or even let them shoot it to see how they do. It may be that your technique is not up to snuff; you would be amazed to see the difference how and where you rest the forend makes on a rifle with a rather springy forend. My Axis rifles do there best if I rest the forend either on my off hand, or on a rest back near the action. Also, Axis triggers are not the greatest out of the box; they are easy to improve, though, and again, a decent trigger can make for astounding accuracy improvements.

I don't really think that just a bit of bedding will hurt anything, but you never know. A bit more experimentation may pay big dividends. And, hey -- if you're killing deer at 200 yards with no problem it's doing the job as-is.