First, welcome to DR1!
A good place to start is here:
http://dr1.com/forums/living/112283-living-costs-dominican-republic.html
It's a long thread, but contains lots of really good information as far as how much you'll need to get along in various areas.
My advice is to take a portion of that 10k, and come down for a month or two. See how you really like it, and only then try to figure out how to make a living in DR. See if you really want the non-tourist lifestyle, or just need to get "caribbean fever" out of your system.
The majority of people who do live here obtain their money from non-DR sources (i.e., pensions, social security, investments, online businesses or outsourcing.) It is very difficult for someone who doesn't have a deep understanding of local business practices and/or come from one of the well-connected Dominican cliques to do well there.