I will have a look at your simple setup, but a more exact one is as follows, which gives you 12v, and limits to 1A exactly whereas your bjt based limiter is inaccurate.
The LED lights up whenever the output current goes above 800mA.
The output voltage will reduce as the load gets heavier, such as to limit the output current to 1A MAX.
The schem is here, but also the ltspice simulation, which you can run in ltspice, just change the .txt file to .asc, and hit the running man icon in the simulator..which is free download