That setup will work... but it's going to be harder on the drivetrain for sure and you may not like how slug-ish the truck will feel. I ran 37's/3.73's in my Cummins for a few months... eventually swapped to 4.56's because the truck just felt terrible. Way too low of an RPM at any given speed, slow off the line, and I didn't feel like blowing up a transmission. Did it work? Yes.... but the 4.56's made a HUGE different and were definitely worth the money.
You can budget around $2500-$3000 (everything in) for a gear swap depending on exactly what you want to do and the local shops in your area. Definitely helps that you have a 2011 so you'd be able to use your front diff. 2012+ guys have to get a front diff from a 2011 to do the swap.