At a glance, I see three classes of animals.
1) Those that symbolise (royal) power - including Persian, Chinese and Indian symbols:
Bull + Bull & fish - Eagle (attacking stag) - Elephant - Fish (1 or 2) - Lion + Lion attacking stag - Peacock - Snake & Dragon - Dragon and the more symbolic Lion & Sun.
2) Those that are popular food:
Bird (unidentified) - Goose - Hare - Goat - Pigeon
3) Those that are transportation:
Camel - Horse
There is apparently a regal streak - not mindlessly copying other people's symbols, but adding elements such as an attacked stag or a snake - and a popular streak, where the animals may be symbols of, or it least referring to, wealth. Since the missing animal is a donkey, I wonder if one of the horses might actually be a donkey. No, chicken are not missing. In that part of the world, pigeons are often preferred over chicken. Pigs and dogs are taboo.
Peter