In general I agree with you that you are approaching the time when she will need/want her own space if it is available. Obviously lots of families don't have extra bedrooms, and girls have often had to share rooms with brothers, but it isn't always easy. Her six-year-old brother's behavior is not abnormal or even inappropriate. He is at an age when it is normal to be curious about the differences between boys and girls, and his mom and sister are the two females he sees the most, so he will try to look. You do need to talk with him about the meaning of privacy and how to respect other people's privacy, but he should not be reprimanded for being curious.
If you have the extra room available, you can start to make a transition by having her use the room for various activities when she wants to be by herself. If she has a sleepover she can use that room as well. Over time you can move more and more of her belongings into the room until she is ready to move there completely. Be aware that she still may want to sleep in her brother's room from time to time, even when she is in her own room.