1. You can file a joint federal return and separate DC returns. Because your wife moved to DC in November, she would only be required to file a DC return if she had to file a federal return for her Unemployment income (based on a federal Married separate return).
2. Yes to file the Dc return separate, you can follow these instructions: How do I prepare a joint federal return and separate state returns?
Because your wife only had the Unemployment income, you may want to file the Joint DC return, you will most likely have better tax results overall. It will be a Part Year return and you would only be taxed on the income you made in Dc or while a DC resident. (The only way to know for sure is to prepare the return both ways, but even looking at the time savings it seems you are better keeping the joint return.
@stefanz
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