The width is the issue. Your stock tires are about 10" wide. You can't add another 2 inches without trimming the wheel well guards, and even then you'll have some rubbing when you crank the steering all the way. But that's with stock rims...if you get a set of after-market wheels, it's a different story. I still think you'll need some trimming to accommodate 12.5" tires, but maybe not.
This post has info about mounting tires to stock rims: http://www.tundraheadquarters.com/blog/toyota-tundra-tire-size-guide/
But if you're going after-market, you need to talk to the tire and wheel dealer and let them sell you your setup. Just be sure to get some sort of fitment guarantee in writing before you order. That way, if they screw up the math, you're not on the hook.
So, the answer is to ask someone else. :) Sorry about that, but your wheel and tire dealer is the next stop.