Nine is far too young to be having a solitary, romantic boyfriend or girlfriend. Kids at this age and stage are not equipped to handle the complexities and intense emotions of an exclusive boyfriend-girlfriend relationship. I am sure that all her friends' parents are not allowing or encouraging their kids to have such exclusive relationships. Ask them--I think you'll discover that they have the same reservations as you do. Many parents believe it's "cute" at this age to encourage "puppy love." It's not.
Explain why you do not want her to have an exclusive boyfriend, while encouraging her to continue to socialize in groups with her friends. I'd like you to have some discussions with her about why she feels the need to have a boyfriend--is it to be popular, to keep up with her friends, to be noticed by boys, etc. While discussing this topic, work in some questions about how she's feeling about other aspects of her life--school, social life, extracurricular activities.
Also ask her how life has changed for her since her brother was born. Put yourself in her place and talk to her with empathy and understanding, not blame and disrespect. As you continue to make her feel special and stay in touch with what's important in her world, you'll learn better how to counsel and understand her.