I tried to use jetstars online booking over a year ago and had the same problems, tried IE and then firefox no luck. In the end I had to book over the phone and the Jetstar guy was in such a rush to get he miss spelt me name and address and when I tried to ask him a question about the credit card charge, he ignored my question, just kept asking for my credit card details, and actually had to ask 3 times before I got a response.
Was very frustrated once the itinerary came through with incorrect details I wrote a letter to complain, only to get a response from jetstar "Jetstar are sorry that you made an error in your booking" yes that’s right they said it was my error.
Going on another holiday now and thought I'd give them another go because they were cheaper however online system not working again, despite trying on different computers, now willing to pay more and never fly jetstar again!