Can a defendant be sued for punitive damages following a DUI auto accident if they served 1 year in jail?

First, if a lawsuit was already filed by the plaintiff:
1) If the lawsuit has been settled or resolved, that's it: once the case is determined, you cannot sue for more or again for the same act or incident. Under the "entire controversy" doctorine, all claims had to be brought together, in the same case, and claims not brought then are given up forever.
2) If the lawsuit is still going on, you can add a claim for punitive damages if you are still earlier enough in the lawsuit to "amend" or revise the complaint freely; typically, though, that's only for the first several weeks or few months, depending on your state's exact court rules. After that, you can only add a claim if the court gives you permission to do so (you have to file a motion, or official request, to amend). Generally, the earlier, the more likely it is that the motion will be granted; after discovery is complete, it is VERY unlikely that it would be.
Second, even if you can add the claim, be advised that punitive damages are comparatively rare except in cases evidencing something like "depraved indifference" to life or the consequences, or an intentional attempt to harm another. A DUI might be a situation supporting punitive damages, but it is not certain; much depends on circumstances, like how much over the limit she was, whether there was a pattern of excessive drinking or this one a one-time event. The law, for example, will view differently someone who happened to have one or two glasses of wine too many, vs. a power drinker who has had previousl problems with alcohol.