Contrary to popular belief, quitting your job does not immediately disqualify you from receiving unemployment benefits. The key factor is whether or not you had good cause to quit. If you quit because you decided you just didn’t feel like working, that would probably fail the test. If you instead quit because you were harassed at work, that would often meet the test.
When in doubt, file for unemployment benefits as soon as you can and than talk to an expert about your particular circumstances.