The quest automatically updates and ends, without giving a usual automatic reward.
Moving the dolls will allow you to loot an item from the chest, as a reward:
You have 3 minutes to move 5 dolls to the bed. Moving all 5 dolls to the bed sets a 90 minute reuse timer on the zone and grants the ability to loot the toy chest.
The timer is not visible, but starts from when you received the quest and ends without notice.
There are five groups of five dolls each. Only one of the five dolls in a group will not twitch. If you pick up any doll that twitches, the four 'twitchers' of that group turn into dollies (level 70^^^ grouped).
If you are pick up the wrong doll, you will get a spell casting timer. Immediately interrupt (either by moving or hitting the Esc key) to prevent the fake dolls from spawning. If you get the right doll, there will be no spell casting timer, and the doll will immediately go on your cursor, allowing you to place it on the bed.
If level 70 is gray to you, you can turn all the groups into mobs then move the remaining dolls to the bed.
A discussion page exists which may contain more information