Nadeem,
I work for one of the Middle East Airlines. I know that falcons are permitted onboard for inter gulf flights as long as they are caged etcetera, however I do not know regarding Emirates, but as most Middle East Airlines I know of follow this rule, chances are, Emirates are the same, however don't quote me on that!
as you don't state where you were travelling from and to, I cannot help any furthr, bur 6 years out here has taught me that things are different in this part of the world in certain aspects. I know that we as a carrier do allow Falcons, however no more than two per flight, and only inter gulf, sheikh or no sheikh
I hope this information helps.