All mannequin parts can also be obtained from the Flotsam in your Mog Gardenduring the 11th Vana'versary Campaign. They are not available as flotsam normally, however. If it is currently possible to receive mannequin parts, you will be receiving two flotsam a day, and the second flotsam has a chance to be a mannequin part; additionally, Crabauble will look like Courier Carrie whenever mannequin parts have a chance of appearing in Mog Garden.
Put it Together
Now go back to Mhaura and trade all 5 pieces to Fyi Chalmwoh. You have to wait <s>a game day </s>one earth minute to get your reward.
It is one GAME day. I just did this quest, traded at 23:30 Lightsday and receiving it the next game day, Darksday.
She will give you the mannequin that is the same Race and gender as your character. If you want a different mannequin, trade the one that you have back to Fyi Chalmwoh and she'll let you choose another one for 2,000 gil.
Once you've completed this quest, you will now be able to buy more mannequins from Fyi Chalmwoh for 100,000 gil each, or you can trade in one that you have to get one with a different race or gender.
To place equipment on the mannequin, put it in your Mog safe and arrange it like normal furniture. Then place the equipment you want to use in storage. Go back to layout, select the mannequin, and select <Equip> from the menu. You can now equip the mannequin with the items in storage just as you would equip yourself with items in inventory. However, only equipment that is normally visible (Main, Sub, Range, Head, Body, Hands, Legs & Feet) can be used. Note that you will need to unequip an item before you can move out of storage. Also note that items still use up storage slots whether they are equipped or not.