If you don't have the source code, then you will have to do one of two things:

1) disassemble their source code
2) try and "emulate" its functionality

either way, once you've written it and handed it over, the best thing that will happen is that they will then profit from your work and will not give you a cent, the worst that will happen is that they will sue you for disassembling their code.

If you try to emulate their functionality, then there's bound to be something you miss. Moreso if you've never programmed before.

Not to shatter your dreams of being a prospective driver writer, but this is not a project I recommend you pop your cherry on.

Look at it this way: you are going to spend the next year of your life learning to program and emulating the functionality of a driver, for which you will have to do extensive testing, debugging and fault fixing. Even then, you may still find serious bugs years later for something critical and on top of that you will have spent a year on something that has no support whatsoever.

What would your annual salary be if you were a junior programmer? Would it be cheaper to just buy a cheap PC, install Linux on it, and just run their software?