Unless you are applying for an exemption for Domincan citizens living abroad or have a very good connection in Aduanas, forget it. Aduanas will charge you taxes for more than the value of the furniture. If you think you have something that qualifies as being covered by Cafta, you can call the Aduanas office as found on the webpage and ask them personally.
Shipping is not the only consideration, as noted in the other post. You can ship direct with Crowley, Seaboard, Antillean or Tropical lines. All go to both S.D. and Puerto Plata. You can also ship less than container load (LTL). A forwarder may be able to negotiate a lower rate than you can get yourself, but may also end up costing more with their fees. Call the line direct and ask the rate department for the Southbound rates for 20' and 40' and LTL (if available) to Rio Haina (S.D.). LTL probably would not be good for furniture (they charge you by cubic space, not weight generally). Check this site for starters: Container shipping to the Dominican Republic (D.R.) and Haiti – ship your containerized cargo to and from the United states (u.S.), including apparel (807 / 9802), pharmaceuticals, refrigerated (reefer) perishables, vehicles and freight of all . Your greater concern is to get a broker in S.D. to get the goods released. One option is to use a freight forwarder that has offices in both Miami and S.D. (M.I.F., Caribex, for example) but the door to door charges from a freight forwarder always seemed much more expensive than when I ship direct. A good starting point is to call one of the forwarders who do their only clearing in S.D. and request a "door to door" quotation for your merchandise.