The mooncloth robe is lovely! I recently got the recipe and mats on my tailor as I wanted this tmog for my Vulpera priest (snow white fur and white robe screams holy priest!). I got very confused with the Wowhead comments on getting this recipe, but no key or lock picking was needed to get to the vendor in Dire Maul. The list of steps Dottie gave matches up with my memory of getting to the vendor.
To get the felcloth needed, I had most luck farming misty grell in swamp of sorrows. This guide suggests winterspring is better but I did not have much luck there: https://www.wowhead.com/guide=843/felcloth-farming
The recipe for mooncloth is bought in Everlook and you just need to take the felcloth to a moonwell to turn it into mooncloth. There are moonwells in various locations (you might remember them from lunar festival quests) - Ashenvale and Feralas off the top of my head.
I only have the pattern on Horde Emerald Dream - Terenas so can’t help directly. Good luck getting it - it’s a really lovely mog!