I always wanted a boyfriend, too, but surprisingly, I never really had one. Of course, I had the benefit of having an older sister and brother. When I would try flirting with my brother's friends, they would tease me and my brother would get annoyed. My sister helped emphasize that boyfriends at that age are silly because they are so immature. She was right. It's not until guys are adults that they usually understand how to properly treat a girl, and even as an adult some men don't get it.
Try pointing out all the careless and insensitive things guys do at that age. Also, let her know that the best boyfriends start out as friends. You might want to ask her why she wants a boyfriend, although she may not know. If it's because she wants someone to care about her, point out that guys don't really care at that age. If it's a status thing, mention that the guys worth having are the ones that will respect you for being yourself. If it's for physical reasons, think back to your first experiences. I know my first kisses were disgusting. The guys slobbered on me and gave my tongue whiplash from all the movement. :)
Good luck! My parents told me I couldn't start dating until I was 25, so I don't think you're being harsh. At 11, you're just starting to notice the bigger world around you.