AF and an item level 55+ weapon are all you really need for AK as a healer IMO. Especially considering the place drops the level 60 armor sets that would be an upgrade. If you absolutely need an upgrade over AF, you could still make do with the crafted level 55 set, especially if it's HQ... and heck, you can actually make money spiritbinding those sets into materia as you do the many, many dungeon runs you'll be doing for endgame. The set in question is as follows:

Weapon: Madman's Whispering Rod
Head: Imperial Operative Hat
Body: Imperial Operative Dalmatica
Hands: Militia Ringbands
Waist: Militia Belt
Legs: Militia Tights
Feet: Militia Duckbills
Ears: Militia Earrings

Fill in the remaining accessories with level 49 HQ crafted stuff, either Turquoise or Tourmaline depending on whether you prefer spell speed or MP.