Why is the GDP a good base for determining a budget at all? To me it looks rather like a variable that tells you something about affordability than about necessity.
Another imperfect metric! Personally, I like defense spending per capita. Reducing our spending by 25-50% would put on on par with Europe and that would give us an idea of what our capabilities would be with that level of spending.

Today we are back to our geo-strategic roots, and arguably the period of time from 1900 -1941 is far more applicable to our current situation than the period of 1947-2012. Did you look at that era as well?
Except we still have our Cold War defensive alliances. As long as we're obligated to defend allies around the world, then we'll need the capability to project power and deploy combat forces to those areas. That's not cheap.

Also, it's putting the cart before the horse to simply declare that we only "need" some amount of defense spending. Can we have the capabilities we have currently at 1% of GDP? No. What will 1% get us and what will our alliances and foreign policy look like if spending was restricted to that amount?