The ilevel of the gear matters a lot, you will notice a huge difference in the damage and healing power. The healer job quests often requires quite a bit of dps from the healer in addition to healing, and that's where the ilevel will make a significant difference. Don't forget to put cleric stance on your hotbar to toggle between dpsing and healing, this could also help a lot in the quests that require you to dps as a healer.