Welcome to Tnet. No, it couldn’t be antique (more than 100 years old). Vintage (more than 50 years old)… yes. Many sources say that Henry Talmadge Link established the Dixie Furniture Company in 1901, but that can’t be true. Link was born in 1889 (died 1983), so would have been twelve years old at that time. The company was indeed founded in 1901 but it’s association with Link (formerly a banker in Lexington NC and New York) began in 1936. From 1940 onwards Link took it from a small company hand-making wood furniture to a much larger business utilising mass-production techniques, pressed wood and laminates. The company ultimately became “Lexington Furniture Brands” but is no longer in business as a manufacturer. I believe they stopped manufacturing in 1986/7.
Furniture with the “Henry Link” embossed name usually has another mark somewhere else as an ink stencil, so check underneath the drawers and the bottom of the carcass. If there is another mark that may help date it more precisely, but sometimes the mark says nothing more than the range style. Your vanity is in “French Provincial” style, which made its first appearance in the 1950s, initially in varnished wood. Factory-painted finishes began appearing in the 1960s and remained popular into the 1970s.
I would think a dealer might be asking around $200 for a piece like that at ‘showroom’ prices but as a seller you would probably get a little less than half that providing it isn’t badly chipped and hasn’t been re-painted.