I'd say a crane is a pretty good guess though, given it's a falconry picture; Wikipedia says
> The common crane (Grus grus) is generally believed to have been a breeding bird in Britain in the Middle Ages. English people prized cranes as the "noblest quarry" for a falconer, and gladly ate them. In December 1212 King John flew his gyrfalcons at cranes at Ashwell, in Cambridgeshire, and killed seven, and on another occasion in Lincolnshire in February 1213 he brought down nine.
https://www.rspb.org.uk/whats-happening/news/the-great-crane...
DQ was written in like 1600 but based on chivalric romances from 200-400 years earlier, where it turns out ostriches also come up from time to time, even in heraldry of some characters.
Basically what I came to is that southern europe of that time had a high degree of exchange with other mediterranean cultures including asia minor and northern africa where ostriches were present. And these seafaring cultural and trade spheres also extended into nothern europe and the british isles.
So ultimately I don't think they were going off the bible for it. It's no more unusual than someone from that area being aware of lions or crocodiles and their general appearance. It would probably be very unusual to have seen one, but they would appear in puppet shows and travelers tales for sure. Literate people may have seen them in manuscript illuminations as well.
There were people in England in Anglo-Saxon times. who had been as far away as Alexandria, or Constantinople.
Icelandic sagas in the late 1000s, wrote about William the Conqueror in England, and noted that many of the surviving Anglo-Saxon nobles fled to Byzantium. So, even in Iceland they knew about Constantinople, and probably ostriches too, and that these were real things and places, which you might travel and see, even if they were basically at the other end of the known world. At the other end of the world, Byzantine records mention Anglo-Saxon warriors being recruited at that time.
People got around even back then.
It's much less likely there were live ostriches in Anglo-Saxon times but the rich have always enjoyed mangeries and exotic animals. I wouldn't be surprised. And there would be traveller accounts and stories, increasingly mythical to be fair, as large population movements from places where people had actually seen them declined in the post-Roman era.
England was never part of the roman world. It was the collapse of the roman world that allowed the anglo-saxons to settle and create england. England was a post-roman world creation. Heck it was part of the destruction crew of the roman world.
https://en.wikipedia.org/wiki/Roman_Britain
USAmericans tend to say "England" interchangably with "United Kingdom", "Great Britain", and "The British Isles". Possibly more.
Also, people very commonly use the name of modern day countries to refer to their territory, such as "most of Germany was frozen over in the last Ice Age". I suspect this is what is happening here.
Possibly peafowl? They were kept in medieval England. There is some bright decoration on the head. The head and legs are too long, but other things in the picture are not to scale either.