That dresser is in very rough shape and I'm not sure its worth the time and effort to restore. That said, the hardware is called Hepplewhite style (sometimes Sheraton style) bail pulls. Test with a magnet to see if they are made of punched brass or steel (steel is more likely). Note the distance between the screws. You should have no trouble finding pulls that fit and are close in appearance on ebay - but you may not find an exact match without spending some time looking. You could also try retail hardware stores like http://www.houseofantiquehardware.com/federal-drawer-pulls-medium-hepple... or http://www.horton-brasses.com/hepplewhite.asp
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