Short answer. Yes, you can. But, I will mirror the comments about payload capacity. I tow my trailer with a Tundra. My GVWR on the trailer is something like 7200 and I regularly go down the road with about 6500 as a trailer weight. I have stopped and measured this a few times.
The Tundra is rated to two 10K but..at this is the challenge with all half tons, it only has a payload of 1700. With my WD hitch I will drop very close to 900 pounds on the ball, the two of us come in about 350 which doesn't leave much room to pack things into the bed. I am find with axle loads and GCVW numbers. The Tundra tows nicely and it has plenty of power to handle mountain passes.
I have heard a lot of positive things about the Eco Boost engines. Watch your payload and you should be good to go.