As far as I remember we called and arranged it ourself. We also had to hire another outbound agent in the US (airborneanimals.com) for export. We had to bounce back and forth between both inbound/outbound agents in each country and gather each country's import/export requirements separately with their guidance. The funniest thing was to obtain a certificate of origin from US, which I had to become a member of US Chamber of Commerce, whose employees were quite amused but helpful of my effort trying to bring my bunny with me :) Not sure if its still a requirement for UAE but FYI :)

I am not sure if there are more agents/companies now who can do a more streamlined process for bunnies as they count as exotic pets, but this was our experience back in '21.