Your mirror does not have to be the same width as your vanity cabinet. Houzz has lots of bathroom pix where you can get an idea of what may work for you.

Some considerations:
1. Are 2 people ever in there at the same time trying to use the mirror? If so, then you'll want the mirror to be pretty wide, but no wider than the vanity.
2. Does your small closet have enough storage for meds, daily toiletries, etc? If not, then you might want to consider using a medicine cabinet. I think you can get one about 30" wide from Lowe's and that should house most of what you'll need.
3. What is the style of your bathroom? You may want to go with a decorative mirror that restates that style.

Best of luck.