A useful material which has nothing to do with animals is
buckram - a stiff cotton cloth, soaked in a sizing agent such as wheat starch and is used in bookbinding, curtain headings and hat making.
It is formed of 2 words, both words are animals
buck - a male deer, antelope, sheep, goat, rabbit or hare & ram - a male sheep
... but another possibility is the very common word ...
carpet - carp the fish, overlapping with pet which may be various kinds of animals