Let's back up and start with why a 1MOA target, why a Savage Axis II XP, why the 30-06, and ultimately what are your goals/needs/wants in asking this question?
A direct answer FWIW - I've hit 1MOA targets, at 1000 yards, with 30-06, using a cost-effective rifle, and using factory ammo..... just not all of those at the same time. So you could make it happen, eventually. Going to be a very long and probably painful walk to get it done when there are other options out there. My first long range experience was with a Bronwing A-Bolt in 30-06 with a 7 power scope, and I got a lot of mileage out that combination.
Are you open to changing parts of the question to make the journey easier on yourself?
Or do you want help making the best out of a very particular set of facts?
We can help with either, just let us know a little bit more please.