My Healing Priest really hasn't done much in the way of quests all through her healzorz life.
I started healing full-time for PUGs of complete strangers at about level 35 after having traded run after run with various friends of mine to get her up to that point while she was a toon that I didn't focus on very often and mainly only played to burn off rest bonus here and there.
PUGging worked great (especially those late-night ones) all through the 30s and 40s, but once I got to the point where Blackrock Depths was the main instance to run through, things slowed way down, and I finally bit the bullet, went shadow for a while, and ground my way from 52 to 58.
Once I hit level 58, I re-spec'd back to Holy/Disc and started healing Ramparts and Blood Furnace runs in Hellfire Peninsula. I didn't touch a single quest in that zone (not even dungeon quests) until after I had reached 5999/6000 Friendly with them, and then a quest-turn in from a drop in Ramparts brought me over the boundary to Honored.
After I finished getting to Honored with Thrallmar, I was ready to hop into the Coilfang Reservoir instances, and then into Auchindoun, and up and up from there.
I lived in instances throughout my 60s and, once I hit 65 and started planning for my level 70 gear, in the PvP battlegrounds as well.
Why Holy/Disc Priests Are Generally Poor Solo'ers
I'm sure it's no surprise, but a character like a healing priest with very few points in the Shadow tree aren't anywhere near as uber as most other characters in the game when it comes to questing and in particular, solo questing.
We wear tissue paper for clothing, we have very few offensive spells, and our bars are all set up for healing if we're dungeon priests.
But of course, there's a limit to that cry of "Healing Priests can't solo!", because at some point of gearing, no matter what your +heal gets to, you've still got pretty decent +damage stats as well, especially if you're looking to solo quests a few levels below you.
At 1600 +heals, I also have over +600 damage in the same gear, which is way more than most Shadow Priests have until they get into the level 70 gear themselves.
Soloing Hellfire Quests For Reputation Gain
Reputation gain and quest rewards are two reasons for a level 70 player to go back to the quests they skipped in various zones while they did the Dungeon Scene - the rings and trinkets and other rewards can help fill out off-sets or holes in primary sets quite nicely.
And of course, if you want maximum reputation gain in Outland, you save the quests for after you've maxed out what the lower-level regular-mode dungeons will give you...
So, here I am, grinding through Thrallmar and Spinebreaker Post and Zeppelin Crash Site quests by myself, having a grand old time with my limited arsenal of offensive spells, and smiling wordlessly to myself as I quickly gain reputation that others around me seem too fearful to try to get because they're (not a Paladin) and either Holy or Protection spec'd.
Heck, in Hellfire I can easily take on 3 mobs at a time, and I'm sure there are some Holy/Disc priests of my exact same spec who can do a lot more!
Why Do Them As Holy? Why Not Shadow?
Simply put, I like to be non-standard, and I like to prove that it's possible to do things in a non-standard way and still be successful with it.
Plus, I hope that some of you Priesties out there who are a ilttle afraid of trying to solo some quests on your own will be inspired and get further ahead individually as a result.
I'll let you know when the zone quests start to get too hard for my Holy/Disc healer!