Umm... her W and E use no Mana. Not little, but zero.

Your Level 4 choice is the reason your mana issues are low. A 0 mana first cast of Q, followed by a shield that reduces your need for self healing which reduces the need to more Desperate Plea. Your level 7 adds quicker self zeal at only two stacks, which add to your self healing. Without spending extra mana on yourself, you, as the healer, can focus on teammates and save mana while doing it.