Are Yellow Jacket Stings Dangerous For Babies?

Unfortunately you won't know if your child is allergic until after a sting occurs.  If it has been awhile and there is no problems, chances are all is ok.  but it never hurts to check with the pediatrician,

Generally if the child is allergic, the sting would have affected the child immediately.  I was stung by a bee in my hand and my whole arm swelled up as soon as it happened.   I went to my doctor for treatment. 
 
If the stinger was left in the skin, take the child to the doctor.  Be careful about removing the stinger yourself.  Don't hesitate to talk to the doctor or nurse.
 
Google has information about yellow jacket bee stings and removal of stingers.