Disclaimer:Here's the basic stuff:
Talk to the moogle and get a card.
Trade that card to someone of the lvl/job it asks for, have that someone trade the card to the moogle, then have that someone trade the card back to you. *You must get the card back or you have to start over.*
Repeat 2 more times.
Trade the card yourself to the moogle as the 4th trade (It'll be the job/lvl you were when you first got the card) and you have a robe.
For the +1, just make sure the 3 people who trade your card to the moogle and trade it back to you are all wearing the dream robe.
I found this at http://boards.gamefaqs.com/gfaqs/genmes ... c=25188111
I tested it before posting it here