Yes there is a fitness test done at Flight Screening.
It is usually conducted once the flying phase has been, or is close to, completed.
Regardless of which service you are applying for or have preference for, you will be tested according to the Australian Army fitness requirements. These can be found on the Army's website or at any recruiting office.
The fitness test will not affect your Flight Screening results - it is an independent test. As far as I am aware, should you fail you will be required to pass it before you can be eligible for selection should you be recommended.
A quick note on the beep test: You will be stopped once you have reached the required level. You should be able to do more than this level though, to allow for a degree of exhaustion after an intense fortnight.