In my opinion, there is no specific chronological age at which kids suddenly are old enough to date unsupervised. I do believe parental approval of dating unsupervised is more a matter of officially sanctioning it since you and I both know that kids can always find ways to get together alone without our knowing. When we allow and/or approve it we are telling our kids that we believe they are mature enough to be trusted with this behavior.
If parents are honest with themselves, they will acknowledge that their children's sexual activity is at the core of most unsupervised dating worries. Are we sending a message through our approval of our son's/daughter's being out alone with a date that we think they are old enough to explore their sexual urges with another?
It's very different for you to drive your 11 year-old daughter and her "date" to a movie, leave them there and then pick them up after the movie and bring them home than it is for you to let that same 11 year-old stay at her "date's" house for the evening when the boy's parent's are out of town.
This question is best decided by first examining what your worries are, if any, about your child dating unsupervised. If you give your permission, but make your child feel like he/she is up to no good or grill him/her about every aspect of the date, then you are sending a mixed message and undermining the positive social development aspects that can come with the initiation of unsupervised dating. Fathers' are famous for telling their daughters to have fun on their dates, thinking back to what they hoped would happen on their adolescent dates and then making their daughters' dating lives miserable.
This is another one of those letting go stages, wherein your natural worries about "what could happen" are balanced by your close, loving, trusting relationship with your child. Trust yourself on this one, Bob; I'm sure you will make the appropriate decision.