Hi , munhann, first , Q2 in the emitter cannot be A1015 because it's a NPN transistor. And find a higher current transistor, this has max 150mA, find one rated to at least 0.5 A
Between the battery and the IR LED you have D1 and a darlington transistor this goes to at least 1,6V voltage drop that leaves only 1,4V for the IR LED. You better leave D1 and use just one PNP transistor as in the datasheet.
In the datasheet I see three diodes from pin13 to pin 10 , 11 , 12 , leaving the pins 11 and 12 floating may have unexpected results.
And finally , don't forget to put a 2 ohm resistor in series with the IR LED because you can burn the LED if you didn't already.
After fixing this use your webcam to see if the emitter is working.