The Doppelganger can't because the Mimic Talent (0) action that the Doppelganger has specifically says (red for emphasis):
(0) Mimic: Target a model within 8” and LoS and choose 1 effect. This lasts until the End Closing Phase. Effects that reference a model by name cannot be Mimicked.
So the ability to summon a wicked doll is on the wicked doll's card saying that it can be summoned by the
Create Voodoo Doll action. So Zoraida can summon wicked dolls herself, and since it's not the Voodoo Doll totem, you can summon as many as you want (though you're probably better served by getting them from elsewhere). The problem is that the Doppelganger can't summon the Wicked Doll because it is named specifically in the ability (I don't have the Wicked Doll's card on me, but I believe it "replaces" the name Voodoo Doll with Wicked Doll.
In anyways, here is official word from Ratty, one of the rules marshals (His and Keltheos's words are law on Rules Discussion).
http://www.wyrd-games.net/showthread.php?26585-Doppelganger-and-Zoraida