DFW is a fair distance away from the city, so you'll definitely need a good chunk of time to get there and back, especially using public transportation. But 12 hours should be enough.
Google Maps has excellent coverage of the public transportation options in Dallas, and shows that to get from DFW to the Dallas Museum of Arts in down town takes nearly two hours, depending on the time of day and which route you take.
With a 12 hour layover, plus 4 hours commuting, and wanting to return 2 hours before your flight, that would give you roughly 6 hours to see down town--so it's doable.
If you want more time, you might consider seeing something closer to the airport.