I would strongly advise against doing any job as a resident that required you to purchase your own malpractice insurance. Instead I would look for an institution that can and will cover you.
1. Most insurers want someone to be at least board eligible.
2. I don't know that you'd make enough as a moonlighter to justify paying for it.
3. It's just a huge headache because you're going to have to make sure that you have a policy in place to cover possible malpractice claims that occurred during that job for years after you have that job. This means you either need to buy more expensive insurance at the outset that covers this or when you're finished the job, you need to buy "tail insurance" in addition, which is also crazy expensive.
Of course my dislike for stuff like this is why I am a happy W-2 employee rather than still out on my own (my tail insurance for my year and change of solo practice cost me over $9,000). If I ever leave my current employer, they buy the tail for me. Gotta love that. 🙂