Iraq has 2 tracks for green card processing. If you are of certain minority ethnic background, you can claim refugee status and fast track your application. The other track is more time dependent. However, priority dates for Iraqi citizens or Iraqi Austrian dual citizens may not be considered the same as for dates for Indian Nationals. Population of Iraq is 37 Million, while India is at 1.3 Billion. USCIS has a priority date by country info tab on its website.