I've done the experience with my father once and there's some paperwork to get ready before. You must own the vehicle which means the title has to be under your name, if not an authorization from the owner approved by a notary will be required. Also you must have an authorization from the police deparement that authorizes your vehicle to leave the country (in this case Haiti).
Now on the Dominican side of the border you will need to get the authorization for your vehicle to legally circulate. You will also have to pay for insurance in the Dominican Republic, taxes or fees . These authorizations will be valid for your expected journey in the Dominican Republic, keep in close look the expiring date to avoid any trouble.
Driving to your destination in the Dominican Republic you will encouter police and military checkpoints that will ask you to show all of your documents. Be very careful on the road and only stop at what looks like legitime checkpoints. If you arrive at the capital don't be surprised if the Dominican Police stops you frequently, they're just making sure it's not a stolen car coming from Haiti.
That's all I can remember from my road trip to Santo Domingo this summer.
PS: I wouldn't recommend you travelling on your own
