Unless you are a veteran player who wants to revisit low level instances for fun, do not look for pick up groups before you are level 70-80. Most low level pick up groups are an exercise in misery for a healer because: everyone is off spec (specialization) for their class, no one is well geared and many are still learning how to play their class.
Wiping repeatedly in the Dead Mines, Wailing Caverns or Scarlet Monastery is not going to advance your healing career. Skip the low level instances unless you have a higher level character to run you through for the sake of getting some exp, gear and quests. The only exception to the rule is if you have found some experienced players who want to work on their low level characters. Finally, it slows down your leveling while you wait for a pick up group and even more time consuming when they go AFK (away from keys), leave early and fight over loot.
Tags: priest leveling guide