I think this might be difficult - not many Q animals - Quetzal bird, Quokka, Quoll (both Australian marsupials) or even a Quagga (an extinct species of zebra). So it is backs to our feathered friends and the Quail.
Woodcut of Quails for a book illustration by Beatrice M Christy
A contemporary American wildlife artist and printmaker. She was born on Michigan and studied painting and printmaking at the University of California - See her website for more information - Link
"Quail in the Field"
Mildrd Nungester Wolfe (1912-2009)
Another American artist who during the late 1960's and 1970's created about 40 wood and lino cut relief prints. These are now available again, having been re-printed from the original blocks. Link . She has her own page on Wikipedia, so I assume she was fairly well respected in her day.
As I thought - I'm finding it hard to find prints of Quails worthy of inclusion. Oddly it seems to be a popular subject for amateur printmakers but not for the establishment names. However, I can rely on the Japanese masters to have used the Quail at some point in the last 300 years, so here are few classic Japanese woodblock prints.