Wooden Dresser Year and Worth?

Without a brand name, it will be very difficult to provide a year, as this style of furniture has been made by hundreds of companies over many years and continues to be made today.
This is an inexpensive chest/dresser as you can easily see the material on the back is very thin plywood and stapled to the frame.
This is an indication of inexpensive furniture.

You can always list it with a higher price, with all offers considered, local pick up only and see what the market happens to be in your area.
Many people would go to local stores or Ikea as this style is readily available new for very reasonable prices.