You are correct the P99 QA does not have second strike capability. If you pull the trigger and the bullet does not go off, you either have to do the barest of a racking the slide to reset the striker (for a second attempt) or do a full rack and cycle the unfired round out. My vote is for fully racking the slide and dumping the round.
There is an indicator in the back. -I'm going from my memory of the standard P99 here, so my apologies to people with the standard P99 if I recall your indicator feature incorrectly. The P99 QA differs from the standard P99 in that the indicator does not extend beyond the hole as it would in the standard model. You cannot feel it in the dark to determine if the striker is cocked. You have to look down and see the red dot. When the gun is decocked, the indicator recesses into the slide so the red dot cannot be seen. If there is a doubt in either direction as to the state of the weapon you can do partial rack of the slide to reset the striker (if it's already set, no harm) or press the decocker to decock the weapon & render the trigger safe.
As far as the QA trigger goes, the striker starts from a partially cocked position (like a Glock- doesn't help, I know). (1) You rack the slide. This action partially cocks the striker. (2) By pulling the trigger, you fully cock the striker and release it in one motion. This state differs from SA because in SA a pull of the trigger releases a fully cocked, set striker. After the gun goes off, it resets with the striker partially cocked. It is never able to transition to SA or set at SA with a partial pull of the trigger. If you release tension from the trigger before it breaks, the striker returns to its partially cocked position. Since it's not true SA, Walther calls it Quick Action. Glock refers to it as Glock Safe Action.