Current limitation of a power supply by using transistors
If you short the output terminals then Q3 will be dissipating 250mA * 11.3V = 2.8W. 

BSR14 is an SOT-23 transistor with an \$R_{\theta JA}\$ of 357°C/W (typical layout) so the junction would head for >1000°C, without pausing at the absolute maximum temperature of 150°C. That would tend to be terminal. 

If you replace Q3 with a much larger transistor (with some kind of a heatsink) then it should survive an output short of substantial (or indefinite) duration, depending on the heatsink. 

Note however that that if the output can be shorted to your circuit ground, then it bypasses the current sensing and the output current will not be limited at all except by the gain of Q3 and the power supply. 

If you could put the current-limit transistor directly in series it would avoid that potential problem. For example: 







simulate this circuit &ndash; Schematic created using CircuitLab

You still need a BFT (big fat transistor) for the output driver.