It is very possible for your baby to get a yeast infection of the mouth also known as Thrush, or a form of skin yeast infection during the birth, as they pass through the birth canal if you have a vaginal yeast infection. Their immune system is still very weak and they are not able to fight the fungus very well yet. However it really is not something to worry about unless your baby is born very premature and is a very low birth weight. It is common for babies to be born with Thrush, the hospital will treat it and you, it is not something you should feel guilty about or upset over.
However if the baby is a very low birth weight this puts them more at risk of a more severe yeast infection, and does come with a fatality rate. But this is only for very premature and low weight babies.