Can I obtain Permanent Residency if my husband is unemployed and I have a work permit through DACA?

You did not mention if your husband is a US citizen or permanent resident. If your husband is a US citizen and is petitioning for you, he has to sponsor you. If he is unemployed, you will need a joint sponsor. Also, you may not need a sponsor at all if you worked for 40 Social Security "quarters" (i.e. earned 40 "credits") in the U.S. (approx. 10 years). For that you will need to discuss your case with an immigration attorney in private.

Regardless of your income, you will need to convince USCIS that you will not become a "public charge." To avoid becoming a public charge, your will need to provide USCIS with a sponsor for you; that is, someone who can support you financially. That sponsor will need to file an "affidavit of support" showing that he/she has an income level at or above 125% of the Federal poverty level. (Even if as in this case, you are the sole earner in your family). You will absolutely need a financial sponsor to apply for adjustment of status through an I-130 (through family), which is what your questions suggests is your situation. Your sponsor need not be your spouse, however. You should contact an immigration attorney to help you plan this out so you can get the result you want,

Maybe. A review of the entire case is needed. A lot depends on the manner in which you entered the USA and an immigration status of your husband. A lot also depend on your immigration and criminal history.

Because you have EAD now, your income is now legal source of income, you should be able to join in filing the I-864 and be counted to qualify for the income level, about $7,500 per person in a family.