It's probably lacquer (manufacturers don't use poly). See if you can take the back off the dresser to get the top unscrewed, it'll be easier to refinish the top with it off. Then strip it with a chemical stripper and refinish either with lacquer, or if you often leave a bottle of acetone there, use poly. Acetone won't damage poly. Good luck finding something to match existing finish - you might find you have to stain it (Natural or other light color) after you strip and sand. To check, wipe it with mineral spirits after sanding (good way to get the dust off) and check the color. That's the color it will be after a clear finish. Water-based poly won't yellow, and Minwax has a Wipe-on version that would be easy - just takes several coats, but dries so quickly you won't have to worry about dust nibs. HTH.

Thank you so much for the detailed instructions. I just about straggled my teenage daughter when this happened!

Have you tried it yet? How'd it go?