The Japanese Dresser in Animal Crossing is modeled after a tansu, a traditional Japanese storage chest that dates back to the Edo period (1603–1868). Tansu were designed to be both practical and portable, often made from lightweight woods like kiri (paulownia) and reinforced with distinctive iron handles and corner hardware. Different types of tansu were used to store clothing, documents, kitchen goods, or merchant supplies. Today, antique and reproduction tansu are appreciated for their craftsmanship, modular design, and the way they combine storage with simple, elegant woodworking.
Etsy has a number of Tansu dressers and cabinets, including this one by Eastern Classics that closely resemble the Animal Crossing version. If the Eastern Classics one is out of stock, try doing a search for "Tansu Dresser", where you'll find many more options.