For 10m I went through all of MSV, HoF, and ToeS without a stam meta, stam trinket, or stam gem. I'm right about 500k now with stam food + agil flask. Don't worry about your HP unless you are a) undergeared for the instance you are tanking b) pushing heavy hitting heroics c) possibly 25m vs 10m but those reports vary.
Considering we have a 30-35% dodge buff (In your face thrash), a CD that cuts 3 atks in half (In your face Overwhelming assault), and Stagger soaks 100% of attacks that do hit basically giving us 100% CTC by default, there isn't much to worry about. Only time I've seen tank issues with my groups was H Gara and that was losing DPS while the DK was tanking, I just hit EB for each Shadowy Attacks and yawned through it (well not yawned I think that fight is incredibly fun as a BrM).
Keeping your buffs up properly and smart use of our limited CD's will get you really far. On magic fights save your CD's for breaths (Fort Brew, Diffuse Magic, Zen Med, Glyph'd Guard), I barely notice Tsulong or H Elegon's breaths. The only fight that really sucks for us in Lei Shi but that fight just sucks all around and doesn't ruin the fact there are a ton of fights we excel at.
Just keep some stam trinkets in your and if a LW some threads to swap out enchants and if EH becomes an issue swap to them. Usually when someone posts "Why am I so squishy?" you look at the logs and easily see it's due to poor buff uptime, CD use, and sitting at high levels of stagger to long.