New car, don't think so.
The information PJT is aware of, is a privately owned car can be imported after it has been documented (registered) in the name of the owner for one full year outside the country. So, for instance you purchase and register a 2006 model this month in your name in the U.S. you will be able to export it to the D.R. in July next year.
The law protects Dominican car dealers from overseas competition within the new car market.
Also, a car older than five years, older than the 2001 model year, cannot be imported into the D.R.
Taxes are any guess as Customs will tax at any rate they see fit for the day.
If you do import make sure that the title for the vehicle is clean and in your name, the shipper. You must have title to the car, not the bank or loan company. The clean title is surrendered at the U.S. port of export to verify ownership of the vehicle it is matched with the authorization granted by the accompanying export documentation. Make sure you ship via a very reputable ocean freight broker.
At the dominican end of the car will be held at the port for processing. Import taxes and car registration fees and taxes must be paid before it is released. Storage of the car at the port impound must be paid also.
Regards,
PJT