How can I tell whether a drone video company is allowed to fly near an airport for my project in Sydney?

Great question, the rules for sydney drone operators fall into two categories

Firstly the Sub 250g category which does not require a REOC to fly within the 5.5km no fly zone surrounding Sydney Airport ( this limits the size of drone that can be flown to a drone that is less than 250grams in weight) and above which will require the drone operator to be fully licensed and will require them to hold a REOC and REPL ticket to fly inside the Airport No fly zone. There are a number of apps and websites that allow you to check where it is possible to fly in Sydney including the Opensky app for Mac and Android and the website ok2go.