It seems like the DD/PDTA114 replacement that you have picked out would work. The bias resistor values are the same, and for a switching application the specific gain characteristics likely won't be important. According to the manual, the Q8002 transistor functions as a switch for switching an IC at an enable voltage of 3.5V, so the difference in voltage ratings is unlikely to matter.
The real question in my mind is whether the short that caused Q8002 to fail in the first place damaged anything else. If there is a fault somewhere else on the board that caused it to fail, then replacing it may only cause it to burn out again, or there may be other problems elsewhere on the board.