Simple fast short circuit protector for circuit
Here is a re-drawn version of your &quot;short circuit&quot; protection circuit.



simulate this circuit &ndash; Schematic created using CircuitLab
First let's consider the switch open state (i.e. there is no short). There is no way for the gate voltage to be higher than the source voltage, so the mosfet will be in the cutoff mode, leaving D2 off (undesired).
Second, consider the switch closed state (i.e. there is a short). In this configuration, D2 is directly shorted out, so no current will flow through it. Similarly, there is still nothing driving the gate of the mosfet to a higher voltage voltage than the source, so the mosfet is still in cutoff mode (now it's indirectly being pulled down to ground via R2 in parallel with R3).
What's not clear is if you intended this &quot;short circuit&quot; to be a fault, or an actual intended mode of operation (i.e. the user pushing a button/toggling a switch). It seems you intend for the first case where this is an actual fault, but then I don't really understand why you're trying to use a MOSFET based design.
If it's the first case, you should probably consider designs which are intended for handling short circuit faults. For example, adding a fuse:



simulate this circuit
If you don't want to replace a physical blown fuse, there are of course other similar options such as resettable fuses (&quot;PTC&quot;), circuit breakers, etc.
If the short circuit case is a desired normal mode of operation, then you can re-arrange your mosfet setup to make it work as intended:



simulate this circuit
In this circuit, when the switch is open, the gate is driven to 9V through R3, while the source is tied to ground. This drives the mosfet into saturation mode, and turns on D2. When the switch is closed, the gate is forced to ground and forces the mosfet to be in cutoff mode.
Note that in this second circuit, when the switch is closed there is current flowing through the switch (albeit, relatively small), while in the circuit with the fuse current will not flow through the short circuit once the fuse blows. This is one of the key difference between these two circuit designs, and why what you intend can change your design.