Amplify µC output from 5V to 12V for external IC that needs 12V to control without inverting
It does look like it should work. With a 5V input at the emitter, T1 base will be reverse biased by about 3V (no problem here for most transistors) and there should be no collector current and TX out will be at 12V. 

With 0V at the input, the base is now conducting forward current and the BJT shouls turn on and the collector will drop to 200mV above the input (if input at 0V then that's 200mV above ground).

Things to watch for - rise time of the 12V out is subject to the speed at which the transistor turns off so if you expect to pass data thru at 1Mbps forget it but at 10kbps (some hand-waving going on) it should be OK.


  Can I use 1kOhm for R3? I have no 2k2 laying around


It should be OK but you are starting to approach the maximum reverse voltage for a B-E junction on a BJT - check the data sheet to see that -4V reverse bias on base-to-emitter is well-within the spec.