There's also the colour "kumral" which is a kind of reddish brown.
My dictionary gives "sparrow hawk" for atmaca and "falcon" for doğan.
I'm not good with bird names either but searching for them in google images helps to clear up some confusion.
As for your translation, it's fine, there are just some small typos in the transcription, which i've marked in red.
(btw, I've also checked my texts again and found more mistakes, which I will go back and correct.)
kalemiye wrote:حیوانلر، دورلو دورلودو۔
Hayvanlar, türlü türlüdür.
بونلر، اکـثاری دورت آیاقلی اولور۔
Bunlar, ekseri dört ayaklı olur.
perhaps this should be اكثری without the extra alef?
بالینہ بو جنسدندر۔
"Balına" bu cinstendir.
بر طاقمنہ: {ییرتیجی} دینیر: آرسلان، قاپلان، قورت کبی۔
Bir takımına: (yirtici) denir: arslan, kaplan, kurt gibi.
not 100% sure, but i think it should be yırtıcı.
آتی
ayı
آیی
قارا طاووق۔
karabatak.
looks like karatavuk here, which is a completely different bird.
From this small sentence there are two words with a tricky spelling. I will single them out now:
کوکرجین - Güvercin. Here ک has the value of v.
Interestingly in Azeri كوكرجین is "göyərçin"; likewise دوكمك is döymək.