The couple had used animal transport company, JetPets to book the ticket on-board the Virgin Australia flight VA785 from Brisbane to Cairns.
While their dog Rambo was safely transported in one piece, the couple have said that they have not been given any answers regarding Cookie's disappearance.
Sharing an emotional plea on Facebook, the couple revealed that they were told that Cookie left the warehouse in a crate.
'I am absolutely heartbroken and just want my fur baby home,' Jessica wrote.
'If anyone knows anyone who works at the airport or lives around the area, please ask them to keep an eye out for Cookie,' she pleaded.
It is understood that Cookie may have escaped from his crate on the tarmac before boarding the flight.
Speaking to news.com.au, Virgin Australia has said they are saddened by the disappearance of Cookie.
'We are truly sorry for this incident and we are doing all we can to locate him,' a spokesperson said.