Strep throat is rare in children under the age of three. That is not to say that they cannot get it but the chances of them developing the condition are low. If you see your child with symptoms of this illness, such as soreness in the throat, or fever, visit a doctor who will be able to correctly diagnose and treat the condition.
The antibodies that babies have continue working for a long time after they emerge from the womb. This helps to protect them from infections. However if your child is coughing, or won’t eat, take them to the doctor as soon as possible.
Source: Mayoclinic.com, "Strep Throat in Infants", http://www.mayoclinic.com/health/strep-throat/AN00949