With respect, you seem to be mistaking references found in some online media sources to usage in a whole country. Getting off the subject a little, but it does have some relevance, the NZ Herald routinely refers to NZ'ers of European descent as 'Pakeha', where as there are plenty who find this pejorative and insulating .. although this attitude is softening. Of course I would not include this in any article (and defintely not this one) without suitable reference lest it be deemed original research, I note it here as an example that the language of the media does not necessarily fully represent that of a country.
What is very important to note is the skewed statistics of quoting the number of 'hits' for rooster found in NZ media. Many of these hits will be refering to the Australian league club Sydney Roosters and not the poultry. Clearly rugby is of very considerable greater interest to the country's readership than poultry.
Just stating both 'Cockerel' and 'Rooster' are used is factual, whereas attempting to define relative usage is reliant on imprecise data, and data that is distorted towards an unrelated subject.
Also, I can see no value to the article in trying to rank relative usage when both 'Cockerel' or 'Rooster' are common.