Assuming that the basic cellular structures of the brain remained the same, you’d pretty much have to assume less processing power of some kind. If you reduce the scale by a factor of (roughly) 6, then you get (again, roughly) 1/216th the volume of gray matter. That’s a lotta neurons. Even if that canard about us using only 10% of our brains was true, your 1 foot human would have a lot less material to work with.
It’s difficult to tell exactly how the intelligence would be affected except by estimating against other mammals of approximately that stature. So figure roughly cat-like intelligence – able to navigate quite well in the world, figure out basic mechanical stuff like doorknobs, but not big on the memory, abstract thinking, and language. There’d probably be sacrifices in perception as well.
On the other hand, reflexes would be lightning fast, as the nerve impulses would have smaller distances to travel.