I went on my first "date" when I was 11!!! I went to the movies to see "Ghost" hahahahaha.... It was so cute, coz we were both innocent and all we ever did was hold hands. Fond memories! I even remember the boy's name!
I think it's ok. My mum has since told me that she actually came to the movie too, sat up the back and kept an eye on us, but I never noticed her and neither did my little boyfriend! hehehe
Just maintain supervision when they are together. Be casual about it - like if they are sitting in your lounge room watching a movie together, pop in unexpectedly now and then and ask them if they want a drink or something to eat. Obviously, don't let them go in her room together, make them stay out in a "general" area of the house where you can keep an eye on them.
Ignore the other mothers - they sound like judgemental cows! They are probably just jealous of your beautiful little girl.
I see nothing wrong with this, as long as she knows there are certain rules she needs to stick to, and what is appropriate behaviour for an 11 year old.
Let her enjoy it - as I said earlier, I have some lovely memories of my first boyfriend - he pecked me on the cheek and I blushed furiously and couldn't look him in the eye for the rest of the day! bahahahaha! I'm sure she's equally innocent and sweet.
Also, you should enjoy it now, coz it's not always going to be this uncomplicated! LOL