I would say.
If you are below 600k hp for normals, get some more hp
If you are below 700k hp for early hcs, get some more hp
If you are below 800k hp for malk/thok/siegecrafter hc, get some more hp
If you are below 1000k hp for Paragons HC/Garrosh HC, get some more hp
Overall, mastery is the stat you are looking for, not stamina.
If you have 547 item level you have absoultely no reason to gem stamina at all ever. I was at siegecrafter HC with 543 item level without any problems, using 0 stamina gems and trinkets. You rhealth levels is way more than enough for your current content.
If you are frequently dropping dead early on in fights at your current gear/progression, the issue lies within how you use your CDs and abilities rather than how you gear it. You only mentioned trash though, that trash can kills tanks so if you dont have issues on bosses there is nothing to worry about.
I would personally look to get the cooldown reduction trinket from malkorok. It is completely awesome for the cooldown part, and also provides you more than enough stamina so you dont even have to think about gemming for more.