This may sound condescending, but it's also true. Don't quit your job with visions of starting off on your own business right away. It takes time. You'll typically need to talk to people, find positions, interview, and get rejected before you find your first good, well-paying contract assignment. You may find part-time work that will not pay all of your bills, but will add to your skills and beef up your resume. You may be able to fit in these part-time jobs around your normal working hours. It's a nice way to make some extra income while getting your name out as a reliable, hard working consultant.

A couple of notes about moonlighting. Do not work on any consulting projects that conflict, even remotely, with your full time work. Do not take designs, code, or any kind of documents from your full time work to your consulting job. And definitely do not use your employer's equipment, tools, or software to perform your contract work. These things are illegal and can put a quick end to your consulting career and, in fact, to your entire career if you should be discovered.