It's tough to put down exact numbers - like I said, spec and playstyle means a lot more than gear in some places.
If you're spec'd for fire and all you cast is frost, it doesn't matter how good your gear is (adjust the spells to your class - the point is the same regardless).
Same thing goes for tanking, healing... if you don't choose the right buttons to mash, it doesn't matter what gear you have.
Before you try for Karazhan, do a few L70 instances (Arcatraz, Shattered Halls, Steamvault) or any heroic with a few different groups. See how you stack up against other people. Talk to the tank, healer(s), other DPS people and see if they think you preformed well enough.
Maybe I'm snobbish, but if I were doing the invites for kara, I wouldn't invite any DPS class that can't do more damage than my healing priest... by a long shot. But I think that's a fair evaluation, because I can only heal for so long before I'm out of mana. If you can't DPS down the boss in that time, we all die.
If you want to try out some instances, just let me know. I've got 3 70s and a 69 that I can take to pretty much any normal instance, plus a few heroics. I'll go along and let you know if I think you're ready for a starter (or even a progressing) Kara run.