I can certainly understand why you'd be worried about a 13 year old girl being with a boy or having a boyfriend. There are many girls at 14 and pregnant. Maybe you should sit her down and educate her about STD's if you already haven't, and if you're comfy doing that... (my mom used facts about STDs to scare me away from having sex and it worked for me..until i turned 18 and first had sex). Maybe you two can make a deal. If she promises you not to date or get serious w/ a boy and she keeps her promise, maybe when she gets to a certain age you can buy her something (probably will be expensive) that she REALLY wants. Just get her to trust you and believe your word (im not saying she doesn't already). At 13 i had crushes, but i never went farther than kissing. Maybe that's all she has in mind, but who knows these days. They grow up so fast
Like i said before, i understand why you'd worry.