Jetstar customer, with almost no rights

So on December 30th at 11pm, I was supposed to catch an international flight from Manila to Darwin then Darwin to Brisbane with my mum and dad. My mum had been vomiting a few hours before the flight time which was mainly caused due to the excessive amounts of travel we did that day (last day shopping). This had us arrive at the airport 6-7minutes after the deadline time of checking in. So we assumed that the check-in had also closed 6-7minutes ago. My mum was no longer vomiting at the time and seemed fit for the flight.

We tried desperately to get our check-in time extended as we really wanted to get home. We were told to ask a staff member in the Jetstar office about the issue. There wasn't a Jetstar office, just another airway office with a guy given authority to act on behalf of Jetstar. We asked him if we could get a late check-in and he replied with something like 'Gate closed at 10. Best you can do is go to Jetstar website and sort it out yourself or contact Jetstar phone support line.' Then he no longer would cater for any of our other questions. He simply walked off arrogantly.

I'm aware that we should have arrived at the airport before the deadline, but at the time, we still logically had 50-55minutes to board the plane. Instead we we're ignored like lost sheep, with no-one to give a damn. We asked about seeing if we could get put on the next available flight to the same location with costs paid for but the first flight attempt, we were told 'No.'. We asked another guy about getting a refund but he said that we'll need medical certificate and other stuff and that it may take more than 5 days to process. This I suppose is fine, but it would of meant that we would of had to make a new booking if we wanted to get back to Brisbane ASAP. We ended up re-booking and we arrived in Brisbane just 7 hours ago. For the re-booking, it was another $2,600AUD for us. We are still desperately trying to claim a refund for our initial incident.

We shouldn't have to pay +$2000AUD on tickets, even though we didn't get to board a flight and get near no customer service/rights at our request and have Jetstar get away with it like nothing happened.