I've allowed my DD, 3, to have a playdate without me at a neighbor's house where I knew the family well and the mom is a pediatrician. But that and the friend who babysits for me are the only 2 so far.
If your DD has food allergies, then you need to inform her of them and teach her. Even my 3 yr old can say, "I can't have apples. They make me sick." and I show her how I read ingredients to make sure there's no apples in the product. I think that you need to teach your daughter so she can feel confident about her own health and life. My DD's little friends have all sorts of different needs and while I learn who can't have milk and who keeps kosher, the kids also need to be proactive in their own lives. Try leaving her with someone you know well who won't give her foods she can't have as a start. I bet she does great.
We can't bubble wrap our kids. When my SD was young, there was a pervert molesting girls right behind clothes racks in department stores. They were in the 7-10 age range. We reminded SD to scream, bite, kick and seek help - and play acted with her. While we kept her close so she wasn't off in the store by herself, it would also do harm, IMO, to make her so fearful she didn't want to do anything alone. Find a balance between your own fears and what's beneficial to your child. I don't recall when SD's first sleepover was - probably by the time she was 7 or 8. In the 8-11 range, sleepovers are common birthday parties. I wouldn't let my DD have a sleepover at a stranger's house (I'm amazed how many parents just drop their kids and don't even talk to you) anytime soon, but her best pal or her cousin? Probably in a couple of years.
My girls are also very social and SD would do things like run off and pet someone's dog. She got read the riot act for that and had to either leave the park or sit right by one of us as a consequence. If they want to pet a dog, they need to ask us, not just go off. But she's a fun, mostly happy teenager now and hasn't come to any harm.