Exporting a queen bee from Australia to Beirut

I live in Sydney. My cousin who is a hobbyist bee keeper asked me to get him an Australian queen bee. I know that Australian laws are very strict on what to get into the country but how about exporting living object such a a queen bee? What is the procedure in this case?

Edit: I am travelling myself, and I want to take a queen bee with me? Would it be possible to carry it with me or perhaps the airline could handle this as they would normally handle a pet? The usual route is Sydney-Dubai-Beirut.