Get a priest.. spam shadow word pain.. and go kill murlocs here, until level 12:
Then walk to redridge mountains and spam more shadow word pain until 15:
At 15 que for dungeons as a healer.
Without heirlooms should take you about 3 hours maximum (not sure maybe less) do to 1-20.
With heirlooms, 45 minutes to 15 and 2 dungeons to 20, about 1 hour and a half.