It really depends on your riding experience and where you will be riding. If you have a calm horse, are a fairly good rider, and are going to be riding trails in a familiar area, I would say go ahead. I wouldn't advise riding alone on the road or in unfamiliar territory, as there is a lot that can go wrong, and as a young rider, strangers are more likely to take advantage of you.
I'm 16 and go riding alone fairly often. A lot of times I'm the only one at the ranch, and I have to unlock the gate when I get there. I ride mostly on the trails around the ranch. I occasionally go on the roads alone, but the ranch is kind of out in the country, where there isn't a lot of traffic. I have had horses for 2 years , but I had a lot of riding experiance before that, so I started riding alone right away. Eleven is pretty young, talk it over with your parents and see what they feel comfortable with. If your parents don't want you to go alone, it is probably best to do what they say, practice your riding skills, and bring it up again in a couple of months.