If you set the time scale to 0.1s=S/div then it will take the dot approx 1 second to get across the screen. If the trace always starts on a positive transition then the trace will be the same every time. You can then see where it moves up/down. You don't need to see a square wave, just where it moves up/down. The way you get it to trigger in the right position is by playing with the trigger values.
BTW, an analog scope can't "display" a 1kHz waveform but just a jumpy dot as you describe. However, your eyes can't see it at that speed so it appears as a square wave. The picture is in your head not on the scope. (For the pedants on here, I know the phosphorous helps but the point is still valid - pun intended).
Mike.