My first RF Transmitter Circuit
Your circuit is drawn in such an odd way that I cannot determine if it might work or not. Besides that, there are no component values so that makes it impossible to judge if it will work or not. I agree that a 2n2222 will not cut the mustard here. There are plenty 433 MHz transmitter schematics to be found when googling for them. Tip: search for "images" instead of "the web".

Regarding the PT2262, pin 17 is it's output, this output switches between 0 V and 12 V (the value of the supply voltage) where 12 V means: transmitter on, 0V means transmitter of.  So just use that pin 17 to switch the power to the transmitter on and off, just like in the example schematic in the datasheet.

I have a suggestion, why don't you just use a ready-made module like this one ?