Yes, as Monique just said, Enchanting is a very expensive tradeskill. If that UD priest of yours is an alt however, go for it.
I usually just solo DM with my Hunter, pick up all the greens and blues that are BoE, then mail them to my Priest Alt. Tons of Dusts and Shards and stuff.
But remember to farm the greens and blues in the places appropriate for the Enchanting Skill of the Alt. If I got a ton of Greens from Scarlet Monastery instead, the Enchantress would only get a ton of Enchanting Mats she can't use for a good while.
Enchanting is also good to combine with tailoring for instance. Then you can train enchanting by enchanting the green chest you just made, then disenchant it for mats again. You will spend more mats than you gain from this, but you will level both skills fairly equally.
But you will NOT be making any money from this at all. Quite the opposite.
So unless you have a 50+ main stashed away, stay away from enchanting completely.