There's a process to getting a cedula. You can't just pick one up somewhere (unless you're the PLD or PRD purchasing votes) but that's beside the topic.
Are you planning on becoming a citizen or legal resident? Information for both can be found by searching on these forums.
The process is actually rather quick. In my case, I had to wait a very long time to get the cedula in my hand but I got my Dominican Birth Certificate quickly.
