Oscilloscope and power supply measurement
NE555 is capable of above 100mA output current in push-pull, so you don't need a bipolar transistor to drive your MOSFET switch. You can use the NE555 output directly. With a push pull driver the FET should switch fast and clean in both directions which means the first µs of your regulator transient response will really be the transient response, and not an artifact of slow FET switching.
You can put a resistor in series with the FET drain to set the load current that will be switched.
Then,

one scope channel in AC mode on the output of the power supply

the other channel on the FET drain, or on the NE555 output


A more useful setup would be to put the resistor in the FET source (if voltage allows) or to use a PMOS with a resistor to ground. This allows measuring exactly the current pulse on the resistor, to make sure it has a flat top, which is important if you want to know you're really measuring the transient response of the device under test, and not the flatness of the test pulse.
I've had problems with this setup before, as there was a tiny bit of crosstalk between scope channels. The regulator transient response was really tiny, so I had to boost scope gain to visualize it, and it turned out the scope crosstalk was enough to screw up the measurement. To test this, move the scope probe from regulator output to nearest ground. If you measure ground, you should see a flat line. If you don't see a flat line, the measurement setup must be corrected. Also make sure the ground of both scope probes is connected at the same spot. If it is not, some of the current may flow in the scope cable shields, and that will add some error voltage on top of your measurements.
If you have crosstalk problems, then don't use the second channel to scope the test pulse, use the trigger input instead.