More transmit power for 433MHz transmitter module by increasing voltage
The device is basically a TX433 rebranded by a few folk and although the data sheet doesn't explicitly indicate one way or the other, page 2 shows it connected to a HT-12E encoder (also running from 12 V) and it could be presumed that the data from the encoder is 12Vp-p: -



Here is the HT-12E spec and the logic input levels are stated as related to Vcc so it's a reasonable assumption that the output levels are also related to Vcc.

Conclusion - you'll need a small driver circuit to convert from 5V logic to 12Vp-p. Maybe something like this: -