How important it is to have a family care plan?

You need one and need it yesterday. That said, get with your 1Sgt and see what the Army requires. Some things to consider are: 1. Does your spouse have access to funds? 2. Are any ID Cards about to expire (yep, that will catch a LOT of Joes unprepared). 3. Where will your dependants relocate to if necessary? 4. Limited Power of Attorney specifying EXACTLY what your spouse can do in your name. 5. Discuss with your spouse the plan.

Be sure to keep it updated.

It needs to be current and in place at all times. You can be deployed NOW! Be prepared.

The simple answer is yes - you need one for your family in the event something happens to you. Things to include: where are all of the important papers (will, next of kin contacts, etc) and making sure they have access to them. List any financial accounts you have, and and creditors who might come calling. Make sure they know who they can contact to get support (your commander, your chaplain, the Red Cross contact, your senior enlisted advisor, etc.).

You also should think about the worse case in that how and where you want to be taken care of in that worse case event.

Also make sure your spouse is listed on your accounts so the spouse has rights to manage them if necessary.
You might want to see the legal office attached to your organization to get this ball rolling.
Your question is a good one - at least you are thinking about your family and the “what if” situations. Well done.