This is not a dresser. It is a wash stand. I believe a bowl and pitcher sat on top. I have several of them and there was supposed to be a towel rack on the back of some of the models. Anyone who knows more, please correct me.

I agree it is a washstand/commode. The chamber pot went behind the little door and the bowl and pitcher went on top. There was one in every bedroom 'way back when.
Often there was a mirror placed above the wash stand. If there was no towel rack there were hooks or pegs nearby to hang linens on.
There were thousands of these and yours is a pretty standard variation coming from late 1800w to early 1900's or thereabouts. Somebody else may be able to place its age better. It looks as if it has already been stripped, so paint away and enjoy it. It looks like it has plenty of life left in it and can be enjoyed in another context for the next 100 years. best wishes!

Yes , it's a washstand . The drawer and door faces are birds eye maple and they are a veneer . There's not a chance it's solid . Birds eye is a very desirable cut of wood/veneer and most often used in the form of veneer .
The glass knobs are not original and yes there would likely have been a towel rack that came with it .
The top "damage" is only superficial and would all come off with stripping and sanding .
If it was mine I would refinish it "natural" with your choice of a clear finish .
I'd date it mid to late 1800's .

Here is my Washstand that I use as a microwave stand. It is very similar. As you can see I use it as a microwave stand. It was missing a couple of the original hardware so I bought and stained these knobs. I keep all my cookbooks in it.

Sharon

Thanks for all the feedback. From looking at the edges, I'm actually very sure that the door and drawers are solid wood and not veneer. In fact, one of the legs also has a lot of the birds eyes maple (the rear leg).
By now, I've stripped and sanded the top and decide to keep the whole washstand "natural." Also, probably replace the knobs and handles with metal ones.

sounds great, please post a picture when you are done with it!

I still need to figure out what knobs and handles to use. Any suggestions? I have all but one of the glass knobs and the screws to attach them.
Other than that, almost done.