I should add, I test drove 4 2011s and they all had it. It was worse on the TRD tires "Rugged Trail T/A"s? and on the All Terrain T/As. I assumed it was that and did not detect it on my dunlops before I bought the truck.....8-(
Does it go away at higher speeds? If so, it is a frequency (speed related) issue and it is most likely a balancing issue. The amount of variation in the balancing skill from tire place to tire place might surprise you. Try some place that only deals with tires. Also, I got the warranty when I bought my Nitto's so I can get rebalanced whenever it is required at no charge.
Generally it is a poor balance job. Nissan Pathfinders are notorious for this also. They need to use a "road force balancer". Large heavy wheels can be hard to get balanced. I'm trying to remember the manufacturer of these machines, oh yeah, Hunter. I seem to remember it's a 9000 series.
Checked my tire pressure in my brand new truck purchased last Wednesday. Pressures varied from 32 to 34 right after driving it. Tires have nitrogen from the dealer. Added air to take them all to 36. Definitely less noticeable shimmy on all the same roads. Running the Bridgestone dueler HTs.