Light Daggers: When Dagger hits a single character with a ranged combat attack, instead of dealing normal damage she may choose to deal 1 penetrating damage and heal herself or an adjacent friendly character of 1 damage.

Light of Healing: Dagger can use Support. When she does, after actions resolve heal an adjacent friendly character named Cloak of 1 damage.

If I use the Light of Healing special power to use Support on Cloak, can he still heal 1 after the actions resolve?
Yes. Nothing in the description of Light of Healing says Support must be used on a different character.

Also, note that it doesn't say anything about the use of Support needing to be successful. All Dagger needs to do is use Support and Cloak is healed; she can completely miss the target of Support and Cloak is still healed.