I assume you've read that somewhere like this, probably with a picture nearby.
My best guess would be the following:
Is used to tell you which picture is meant.
Often if there are several pictures on one page (for example in a magazin), the captions to the pictures will be in one place using "links, rechts, oben, unten" or a combination of those to tell which is the corresponding picture.
Probably refers to the common title of a beauty-queen.
Seems to be a noun–noun compound consisting of the following:
Abuergine - eggplant
haar - hair
plus - plus or in this case with
Zombie-hasen-tasche - Zombie-rabbit-bag
So probably it is meant in a quite mean and sarcastic way, to describe an so beautiful person with weird hair and a curious bag.
Well thats what I would guess from the information given.
After using Google a bit I'm not very sure about the last part any more.
Aubergine could be in respect to the form of the hairs. It looks a bit like sliced aubergines.
But I can't find anything in that picture that would match a zombiehasentasche.
Edit: after Using Google some more, I know it is a reference to another blog entry of that site about a Women with red to aubergine-colored hair and a bag that had a zombie-rabbit printed on it, or something like that.
Em1: Ich bin mal so frei und füge das Foto hinzu ;)
Zombie-Köpfe von Adam Parker Smith. Darf ich vorstellen? Links: Miss AuberginehaarPlusZombiehasentasche. Rechts: icke, Montagmorgen. Dabei kennt der Typ mich doch gar nicht. LINK