The circuit in the yellow box is not as plainly simple as you think because, you want power to be switched to the RF module at the beginning of a data stream and power to stay applied (despite data changing up and down) and then finally, after a short period after the data has finished, you want power to become removed.
This is basically the function of a retriggerable monostable: -
You have to decide how long a gap might exist in your data that you want to to keep power applied for. When you have determined this then you have to ask yourself if, after the data has completed, will this "excess" time at the end of the transmission be a problem. If it is you have to find a different mechanism for controlling power.
If you are OK with this then you might consider using a timer chip like so: -
Taken from here. Clearly you need to then attach the output to a transistor to control power to the radio module. I'd consider an N channel MOSFET that switches power to the negative connection on the RF module. Choose something with quite low on-resistance. If you don't want to go this route and still prefer top-side switching then a P channel mosfet is also good but, you'll need to invert the output of the CD4047 (or use pin 11 instead of pin 10).