The OP's DRK problems almost certainly stem from poor gear.

I made the mistake of entering Cutter's Cry in my level 30 gear and got dunked pretty bad. We made it, but the myself and healer had a few heart attacks along the way.
Upgraded to level 40 gear and all was much better.

There's also the matter where tanks take a lot more damage in general in the later ARR leveling dungeons, especially when you're used to ilvl 110-130 tanks.

As a healer who has healed a number of level 60 tanks, I didn't find them any harder to heal than other tanks. I heal as a SCH.
In fact, all of the bad runs I had were with PLDs or WARs, so it's definitely more of a skill issue than a job issue.