"What am I" vs. "who am I"
Solution 1:
If who is used, the scope of the answer gets reduces to a specific person in particular. Otherwise it has wider scope. So what will be the proper answer.
Solution 2:
The question presupposes a context in which animals are anthropomorphised. Whether one will use who or what depends on how far that anthropomorphising is supposed to go. If one takes it to go all the way, and puts oneself in a fictional world in which animals think and speak like human beings and so ask such questions about themselves, one may want to use who. One the other hand, if the anthropomorphising is no more than a stylistic device for posing questions that test children’s knowledge about animals, then what is appropriate. The authors of the book in question probably intended the latter, i.e. they wanted to pose the question ‘What species of animals is characterised by a long neck and spots?’ in manner that they hoped would be lively.
(This is intended to answer the specific question posed by the OP. The other answers on this page seem to be directed at the much more general question posed in the heading.)