I have this quest: 

I bought this unicorn to fufull it but the drop down menu doesn't appear.

http://beastkeeper.com/pet/942601

Doesn't this unicorn fit the criteria?

It has to be a black unicorn with a normal pattern not cream.

Ah okay, thank you. So does every quest looking for a certain colour pet need the pattern to be normal then?

Not necessarily. "Black" is the full name of the unicorn skin with black color and normal pattern. Some other quests also ask for a specific color/pattern combo, such as a White Gyrfalcon Roc or a Black Bicolor Gryphon. 

But some quests only ask for a certain color and the pattern can be anything, such as a white symurgh. Because there is no symurgh skin called "White", you know it only specifies the color, not the pattern.

Oh, that makes much more sense now! I'll remember that in the future.

Thank you so much! <3

Just to clarify, the color of that Unicorn is Silver, not Black. You can check it on the Stats page. -- If you check the List of Skins page, it'll list all the skins and their name.