Here are some other words for "baby" in Russian, depending on the context:
* младенец (mladenets) - infant, baby
* малыш (malysh) - little one, baby
* грудничок (grudnichok) - baby who is breastfed
* кроха (kroha) - tiny one, baby
* деточка (detochka) - little one, baby (often used in a more affectionate way)
The most common word is ребенок. You can also use малыш or деточка for a more informal and affectionate way of addressing a baby.