You will want to take the same kinds of precautions you would take with any pets: wash your hands after handling them and so forth. Avian and human metabolisms are quite different, so there are few things that affect both humans and birds (even lice that are interested in your chickens are not interested in humans).
However, just like cats, birds can get toxoplasmosis. This is the reason pregnant women are advised not to clean a cat box while pregnant. And for that reason, you may want to have your partner clean the brooder or coop while you're pregnant, just to be on the safe side. Your doctor or midwife may have other recommendations, and I would follow his or her advice on the subject. However, to our knowledge there is no reason you can't keep chickens when you are pregnant. Just use the same common sense sanitation precautions you would use when keeping other animals. (Farm wives have done it for time out of mind.)