I'm just not stupid enough to risk the job I want to have as a career for a side job.

There aren't many restrictions pertaining to what you can do in your down time, but this is one that can get you fired.

If you really want to do it, ask and maybe they'll say yes. If they say no then you have a choice to make on which job is more important.

I honestly don't think you work for a 121 carrier, but if you do and are really doing this, it's just a matter of time.