I think this has just so much to do with the personality of the child. My boys have always been the super, independent, "I do it myself" type. I never taught them how to buckle up, but they were buckling themselves in when they were 2 or 2 1/2 (it's been awhile, so I can't be sure).
I had no reason to try and stop my boys from buckling themselves in. If I had tried to stop them, they simply would have tried harder and been more insistent that they did not need my help. Nothing wrong with me double checking the straps when they were done :-)
One of my brother's girl, while having many wonderful gifts, does not possess the same independent streak my boys do. When she was 5 she had to be taught and encourage to unbuckle her own seatbelt (she was in a booster). I had to delay my boys transition to a booster for fear they would unbuckle while I was driving.
I don't think you're in a hurry to do this, but if she tries to buckle herself in I would definitely encourage her. I think you will naturally come to a point where you want her to be more independent. You'll be able to check what she's done to make sure there are no safety concerns.
Try not to worry too much about these things. Kids have different personalities, and some are going to want to learn certain skills much faster.