Know where stuns can occur (first pull in both Shado Pan and Mogu'shan for example) and plan accordingly.
Brewmasters are fantastic for Challenge modes if played well. Very high dps and great self/group healing. This is from a hit/exp hardcap and then haste stacking perspective. You will have low hp (use agi flasks/enchants/trinkets), and you will be able to carry if dps underperform.
Don't let stagger ticks break you out of invisibility though! I am an idiot and had this happen once or twice.