To get an accurate idea of the approximate maximum current that the circuit is going to take, yes you need to measure it when the circuit is operating, so in your case, when the circuit is sending the IR signal.
As I said before, you should measure the current going into the input of the voltage regulator from your power supply. The meter must be connected between the voltage regulator input and the power supply.
However, don't forget to choose a fuse value that is larger than the current you measure. When you switch the circuit on, the start-up current is usually greater than this.
You won't damage the DMM if you connect it properly. Before trying to measure the current, make sure that the DMM is switched to measure current and that the +ve probe is plugged into the correct socket on the meter for this. Always connect an ammeter in series with the power supply and your circuit, never connect an ammeter directly across the power supply terminals as this will damage it!
SnowyDog