I think you could consider the early "regular" Netherweave (in other words not the Imbued netherweave) tailored pieces. You can learn some of them at approximately tailoring skill level 310. Not so much as a set that focuses soley on healing, but I think it fits the bill.
Netherweave belt-level 61:
http://wow.allakhazam.com/db/item.html?witem=21850;source=live
Netherweave Boots-level 62:
http://wow.allakhazam.com/db/item.html?witem=21853;source=live
Netherweave bracers-level 61:
http://wow.allakhazam.com/db/item.html?witem=21849;source=live
Netherweave gloves-level 63:
http://wow.allakhazam.com/db/item.html?witem=21851;source=live
Netherweave Pants- level 64:
http://wow.allakhazam.com/db/item.html?witem=21852;source=live
Also part of the set is the tunic and robe, but they require levels 68 and 67 respectively, so not really "early" Outland. You can get the set bonus by using only two of the pieces, so you might want to mix and match with various quest rewards, to get some intellect and spirit as these particular pieces really focus on stamina and damage/healing.
For healing in dungeons you can supplement also with AH greens with intellect, spirit and plus healing like "Of the Hierophant", "Of the Prophet" and "Of the Physician".
*edit* Link to the recipes. Scroll towards the bottom of the page for the set I am referring to.
http://wow.allakhazam.com/search.html?q=netherweave#Recipes
Since I am not good at filtering, you will have to disregard the Imbued Netherweave stuff as well as the bandages, but this does include information on the items I posted above, including the tailoring skill required to learn the pieces. Also, most can be learned from the tailoring trainers, which is convenient.
Edited, Jul 21st 2008 5:39pm by Miskreant