Sorry, did you say "a list of the correct phrases to describe various animal calls?" I'm going to have to disagree with that.
We'll start from the very beginning. Bees don't buzz, but they do hum? You might want to report this to the editors of the Concise Oxford Dictionary (Tenth Edition), who are under the mistaken impression that to buzz means "make a humming sound."
Cats mew, purr, swear, and caterwaul, while kittens only mew, and neither one miaows? That's mildly strange, since according to that same Oxford Dictionary, the word "miaow" (or "meow," if you prefer) has been in use since the 17th Century. It also lists "mewl" as an alternative to "mew", stating that "mewl" comes from Middle English - rather a long pedigree for a word that isn't "the correct way to describe an animal call." Meanwhile, every kitten I've ever seen informs me that purring is also quite acceptable kittenish speech. It's worth noting that lions are also known to purr, as are cheetahs.
Deer don't cry? That's really, really strange. This very list tells us that stags bellow. Now, stags are male deer, and "bellow" usually means to call or shout loudly. And "cry", according to Oxford, means not only "to shout or scream loudly", but also "(of a bird or other animal) make a loud characteristic call". In other words, all loud-voiced animals cry. Including stags, therefore including deer.
Geese cackle and hiss? Well, yes, sometimes they do, especially when they're being tormented by visiting dictionary writers. But when you watch a gaggle of geese flying overhead, you aren't very likely to hear them hissing. They will be honking. Also known as "gaggling," according to Wester_1914 and Roget's International Thesaurus (Fifth Edition).
Chickens PEEP? It's becoming painfully obvious that the editors of the Brewer's Dictionary don't spend much time on farms. Last time I checked, chickens mostly clucked, leaving the peeping for their babies, commonly known as chicks. Again, Oxford supports my often suspect memory, defining cluck as "The characteristic short, guttural sound made by a hen."
In general, this list, which purports to list technical names for animal sounds, tends to confuse the names with simple descriptions, undermining its own authority. It also assumes that most animals can make only one sound (this is most decidedly not the case for hawks or apes, which can do a hell of a lot more than merely "scream" and "gibber"). And in several cases, it's quite simply wrong.
With all due respect to the Brewer's Dictionary people, I would suggest that they spend a little time listening to animals if they want to compile the Compleat and Proper List of terms for animal noises. And that they get their facts straight. | 
