Jetstar staff is wasting my time and try to rip me off!

I arrived in time to the jetstar counter but I was told the gate is closed. The staff told me I would have to pay extra $100 to book me into the next day's flight. It's 5:30am and I would have to wait for 24 hours? That's ridiculous. I then found out there were a few people arrived before me and they all got refuse to check in. They were not helping us to check in, just waste time to tell us "No! Gate is closed!". The staff's attitude was so rude as well. I would rather pay extra to virginblue. I'm finally in where I should go via virginblue. jetstar is hopeless!

Domestic
Australia-Melbourne - Tullamarine
Australia-Adelaide