You should start by learning HTML, CSS, javascript. Although not necessary, learning a server side scripting language like Python or Ruby will help. Good luck!
I have a similar problem - i'm studying electrical engineering (currently in 3rd year) but i'm passionate about programming and web development. I recently wanted to switch to software engineering but i realized that switching will be a pain in the ass - i would be delay my graduation by at least 1.5 years + spend more money. Anyways, i decided that it wasn't really worth the changing majors at this point. Instead, i will be attending some software engineering lectures on campus and self teach.
Personally i would definitely take the job, given that the projects that you'll be working on are interesting. Seeing as you are pretty dedicated, you can study / self-learn on the side.
Rather than just copy/paste, study the code and try to understand how the author is doing what he's doing. I study other people's code all the time in order to learn new concepts. Then, you can use what you learned and expand on it in the future. I would also try to apply the concepts you learned from the samples and rewrite the code yourself.