These minions aren't available in-game via normal means and require special codes or extra purchases.

Cait Sith doll
Pre-order bonus.
Note: Some retailers are running low on codes - make sure your preorder code is sent right away.

Baby Behemoth
Collector's Edition bonus.
Note: If you are a 1.0 player and your account is NOT CE you will have to purchase the ARR PS3 CE.

Wind-up Dalamud
"Before Meteor" OST preorder bonus.
Note: The code is supposed to be region-free, but the OST will eventually be available in all regions.

Wind-up Cursor Minion
30-day Veteran Reward.
Note: You should get this pet after your first monthly charge.

Black Chocobo Chick
60-day Veteran Reward.
Note: If you pay for 60 days in advance you will obtain this pet right away.

Beady Eye
90-day Veteran Reward.
Note: If you pay for 90 days in advance you will obtain this pet right away.