I'm sure there are many exceptions, but a good general rule is that children will train pretty much as soon as they are cognitively and physically capable, and emotionally ready to take on the life-changing commitment.
Though there is an early window for many children around a year and a half, they will often lost interest after a few weeks or months, and then it's up to the parents to remember and push the issue (which can result in resistance, frustration, or a sense of failure on both sides). This is far more common, based on my own observations and many, many letters on this site, than kids just training early and staying motivated.
For most girls, training "for keeps" happens at around 2.5 or later. Night training and poop training often happen separately, when physical maturity enabling those stages kicks in, but many children show curiosity and eagerness starting around 2.5 for daytime training. You can certainly begin the mental preparation earlier with books, stories, demonstrating how you use the toilet, playing potty with her toys, etc. When kept fun and attractive, these will enhance the learning process once it actually starts.
When the child is ready, training can happen almost by itself, without charts or rewards, just as learning to walk and talk are natural developments once a child is ready. At that point, the motivators become being a big girl, wearing big girl panties, and being free from messes and diapering. You can start the process earlier, but the child will seldom be truly trained until they are ready. Before that time arrives, it is the parents who are trained to remind the child to follow through.
So whether you start training early or wait until the child shows emotional investment, training will usually be complete about the same age – which varies from one child to the next.