Good luck with a pre-teen girl, by the way and good for you for at least giving it a lot of thought!
My experience growing up was that all my girlfriends could date sooner than me. My parents made me wait until I was 16 then they let a boy take me to a movie and straight home. No dilly dally in between if you know what I mean. I wouldn't be surprised if they went to the theater to make sure his car was there. I hated it, but I was also the only girl I knew not having sex at that age! My mother always told me on our "date talks" "When you grow up and have to face these boys as a woman, you will be able to hold your head high if you have conducted yourself as a lady". You know what, you won't hear me say this about much that my step-mother said to me, but SHE WAS ABSOLUTELY RIGHT! When I went to my class reunion two MEN actually got into a fight because one had slept with the other's wife first. What a shame, but we do have to live with our mistakes. Not just for a minute, but for the rest of our lives.
I think 12 and 13 is WAY too young. You have to be brave and strong and know that you know better than she does, and also better than the other parents who are just letting their kids run wild! She will hate you today, but thank you tomorrow. The big thing to stress is that when she is finally allowed to date, she must conduct herself as a lady, respect herself, and don't be fooled by what a young boy is telling her. We, as moms, have been there in that car with a boy at one time or another, so we know the types of things she will hear. I would focus my time with her now preparing her for that, and just smile, hug her, kiss her and tell her you love her when she is yelling "I hate you, all my friends are dating, etc".
I would also say to offer her a compromise. Let her invite a boy over for dinner and a movie at home (still be vigilant with supervision and let her know you are doing so). My parents did that and it was good. I could have a boy over to visit, and that way I could spend time without any room for error.
I say with things today, drugs, alcohol, diseases, teen pregnancy etc. You cannot be conservative enough, and if that is the worst thing you do to her in her lifetime, she will thank you a million times when she does grow up. I will tell you that as soon as I did start dating, I was offered drugs, pressured for sex and given alcohol, but at 16 and 17 I was mature enough to say no and stick to it! Keep the lines of communication open, though, and be honest with her about why you are making your decisions. She won't agree, but at least she will hear you. I heard my parents. I didn't like it, but when I go for my 20th class reunion next year, I will know that no man there will look at me or my husband sideways (except to think, man, that was the girl I missed out on! :-)
You are asking if it is too young, so you already know it is.