You are working and will have to quit your job to follow your husband can you apply to unemployement in the new state you will be moving in and get benefits?

First, some states allow you to collect unemployment if you have to move because your spouse relocates, in which case it would be from the state you moved FROM (the "liable state"). Secondly, you could not collect from the state you move to because that state did not collect unemployment taxes from your former employer (hence, not the "liable state")