DuCange reports qualea (quail) with qualia (!) and quaquilia as alternate spellings. The work cited by DuCange, by Johannes de Janua, better known as Johannes Balbus (d. c. 1298), explains that the bird got its name from the sound it makes, "quaquera". Possibly this was a medieval development, as in classical Latin, this bird would be called a cōturnīx—apparently also imitative. No word on the vulgo, so it's theoretically possible that ordinary folks in Ancient Rome said something that sounded like qualea, but the word for quail in both the Vulgate and Vetus Latina is coturnix. The OED's etymology of "quail" also reports the spellings quaquila and quaila, and quaccola from the 8th century.
By the way, qualeæ and similar birds are protected by this law in the 1628 edition of the Ius municipale Vicentinum against being caught with nets or hoods during April, May, and June.
The Birds of the Latin Poets by Ernest Whitney Martin (1914) lists one bird whose name starts with Q: querquedula, "probably the Teal (Anas crecca) or the Garganey (Anas querquedula)."
Columella in De Re Rustica 8.15 writes:
Nessotrophii cura similis, sed maior impensa est. Nam clausae pascuntur anates, querquedulae, boscides, phalerides, similesque volucres, quae stagna et paludes rimantur. …
A place for rearing ducks requires similar attention but is more costly. For mallard, teal, garganey and coots and similar birds, which root about in pools and marshes, can be kept in captivity. …
Translation: Forster & Heffner, Loeb Classical Library 407
Varro, in his own Rerum Rusticarum 3.3.3, quotes a playful debate about what constitutes a villa, in which one Cornelius "Blackbird" Merula says that querqedulae need both land and water—important to know if you're keeping them in an enclosure. In De Lingua Latina 5.79, Varro claims that the querqedula gets its name from its cry (or some quality), and that the word originates from Greek κερκήδης. You can judge for yourself here. Note the pitch mark in the Greek word; the pitch and rhythm do seem to match the male call.
So, querquedula is definitely a farm animal and definitely Classically attested.