I'm just wondering if 15 dollars is the right amount of such a task I'm about to be taking?

So, if people here would say, no $15 is too low, you should at least be getting $N/hour, for some N > 15, then what? You're happy with what you get now, will you then become unhappy? Will you ask for a raise? What if you don't get the raise? Leave, and become an unemployed programmer without much experience, and without having ever to finish a project, but with a history of walking out of a project because no longer satisfied with the agreed on pay?