You should claim the JSA as soon as possible because if you don't, it may not be backdated. Self-employed folk can claim JSA but the there are two types of JSA, one is based on NI Contributions JSA(CB) and the other is based on income JSA(IB).
The JSA(CB) is awarded using Class1 contributions, so any self-employed contributions don't count. Even if for whatever reason you don't qualify for the JSA(CB) you may get the income based bit (think of it as Income Support for the unemployed)
It's only folk who have been employed earners who get their JSA stopped for leaving a job voluntarily or through misconduct, so that will not affect you unless you're a postmaster or a limited company director for example.
If you dont qualify for payment of JSA you can still get yir NI Conts credited for as long as you sign on.
So then, to sum up CLAIM IT!