The entirety of ICC is doable as a monk with a 25H LK solo at the end.
Start as WW/MW in 10 normal.
Go through and clear everything except for Valithiria as WW, where you switch to MW (my MW set is 429 with a couple of hierlooms and it still works). Gunship requires a strong strategy and very tight execution even with good gear to solo, to make sure the enemy ship dies before your ship.
Go to your monk trainer, switch one of your specs to BrM. Switch to 25 man (outside of the instance), enter the instance, switch to heroic, solo H LK.
As a brewmaster it is recommended that you have at least 530 ilvl for the enrage/healing requirements to be feasible.