There's a real split here. Side one levels a damage spec because solo content punishes a squishy healer who has no way to kill things fast when the group falls apart. Side two says just heal from level one, because you'll end up doing it anyway once you hit anything like Ruins of Lordaeron or Hall of Thanes and get pulled into a group that already has two would-be tanks and zero healers.
I lean toward leveling damage first, but only under one condition: that the low-level healing kit is actually thin enough to make healing while leveling miserable. If someone can show the early heal spells scale fine solo, my position falls apart completely.
Can anyone who's actually leveled a priest through, say, the Ironforge or Undercity bracket confirm whether solo healing felt viable, or did you end up respeccing back and forth every time a guildmate needed a fourth for a run. Worth checking your own memory against a fresh character rather than trusting how it felt a while back - though I can't say how much things have actually shifted since, that's just a hunch on my part.