I want to know a word for a kid's bedroom just like a women's bedroom is called a boudoir.
Not only is there no special word in English for a kid's bedroom (although "kid's room" implies bedroom), almost no current English speaker will understand "boudoir" to mean "a woman's bedroom." The word "boudoir" has come to be used mostly either ironically or in the phrase "boudoir photography," which means "commissioned tasteful nude or erotic photography."
100 years ago we would say that children sleep in "the nursery" (if a family happened to be rich enough to afford a separate room for the children). For example, in Peter Pan, Wendy and her brothers sleep together in the nursery.
However, now "Nursery" usually means a pre-school (or a place where plants are grown). There is no common single word for a child's bedroom. There is also no word for a woman's or man's bedroom. A Boudoir was a woman's private room for receiving close guests, not for sleeping. (She would sleep with her husband)