Is it safe for me to quit smoking suddenly while pregnant?

Yes. If you smoke you should stop. The faster you stop the better. There is no danger for the baby to go cold turkey.
Yes. And the sooner, the better. Stop with help (nicotine patches, groups) or cold turkey. There is no evidence that it causes any problems to unborn babies at this time. Continued smoking, however, causes lots of problems, especially low birth weight, prematurity and mental problems in the baby, including slower development. Tobacco reduces blood flow to the placenta and the baby. Get help if needed.