Aww I totally understand your feelings here. It's the 1st time so of course you are anxious. All children are different and not every child is off doing independent things.
My 5 are totally different and there's been situations where even though they are old enough on paper to do something, they weren't ready to do it or had never done it.
The 1st are the worst we tend to worry and that's normal. I think once you let them do something it makes it so much easier for future things.
I think all you can do here is make sure she knows who to speak to if she needs to. Explain safety to her, which I'm sure you do already. Let her go and try do something yourself to take your mind off it.
There's going to be alot of 1st in her life, it never gets easier... Sorry... No matter how old they are. It's all about us as parents trying to assess the situation ensuring it's suitable and safe and letting them go and have fun.
I'm still having anxious feelings with my older teens, when they went on a plane with friends, when they drove for the first time, when they went to all night parties etc. Funny thing is, I asked my own mother when she was alive if she worried and she did, she just never showed it, I never knew, I just thought she was a cool mom who let me do many things. My dad said, you never stop worrying, even when your kids are married with their own family...