how do cats do with babies?

hello All, i want to know if anybody has any experience in introducing their newborns to furry babies? i have a cat he is 1 year old and is in our room all the time. i am first time cat owner so not sure abt their behavior. Also i want to know that how do u handle hair fall. my cat is quite furry and has a good amount of hair fall. will that be any issue for baby. Should we keep them separated for few months until baby’s immunity builds up may be a month or two.

p.s i love my cat a lot and i am just asking bcz i don’t want any prob for baby. please share your experience.

my c-sec is scheduled for sunday😊. pic of my cat for attention this is his fav spot to sleep in my bedroom dressing 😂 . my baby will also be in this room as we don’t have a separate room for baby.