Contrary to what many commentators have said, no where in Shulchan Aruch does it say that you make a Shehechayanu when you have a baby girl. The Mishna Berura says his own chiddush that you do make a Shehechayanu when you see the girl the first time, as it is no different than not seeing a friend for 30 days. However, most poskim disagree and advise not to make a bracha.
Upon the birth of a son, the bracha is HaTov VeHameitiv, which is said upon hearing about the birth, not seeing the baby.