Eeeeh doggies, yes, if you are going to leave your job and move to another area with your spouse so they can accept a job offer there, be sure you are leaving CA, (I gather from your posting that you are staying in CA) not most other states. I too checked all the states, tried to find out which others may have this sort of generous approval, may later consult my gurus to come up with this.
In the meantime, CA does pay you if you move beyond reasonable commuting distance (with no transfers available) due to family circumstances. In other words, yes, by all means, if you move from CA to another state or within CA to another area of the state, immediately file a claim as soon as you have a permanent address and are set up where you will be located.
If you left the state, you would still file the claim THROUGH the state you had relocated to, of course if you're still in the same state, it's not an issue, but it will definitely be a CA claim, based on your first four of last five completed quarters of work with a covered employer, which was assume was in CA. As such, it will be subject to all the CA eligibility criteria, all the requirements, amount, etc. of a CA claim, not from the state you are in, even if you moved.
You will be allowed to go to the Job Service/Career Center whatever they call it, in the place you have moved to in order to comply with work registration activities, and of course this is what you want to do.
Every situation is individual, there is no guaranteeing that you will be able to file for unemployment and will be approved, but definitly it is worth your time to file, and you have a pretty good chance from what I am hearing here. The fact that your husband is self employed, is not relocating to accept a legitimate business job offer may be a factor.
It is amazing, the difference between the states in their policies and attitudes toward unemployment insurance/business. If this person was in Tennessee or Florida or Mississippi and filed for benefits, she's going to be told "NO, of course you cannot have this princely sum of less than $275 a week! You chose to relocate with your spouse!" They call it being "business friendly." But in CA, not only is the weekly benefit bigger, they let you have it for lots of "compelling family reasons," for which most states choose not to pay.
Several states other than CA will allow unemployment insurance in the circumstance of a military spouse transfer. But I'll check more later on the general relocating spouse thing.