Hi E.! I wanted to begin potty training my son early too as he was walking and running by 9 mos as well, however I was strongly advised by my pedi to wait until he was 2 b/c early potty training could cause delays in other development. I believe you can start earlier with girls(around 15-18 mos).
I was also told the earlier you begin potty training,the harder it is. For the best and quickest results, a parent is to wait until the child is able to express that he/she needs to potty and is able to hold it until they reach the potty. My son will turn 2 at the end of this month and I am now reading up on my how to books for potty training boys. I think he's ready b/c everytime I change his diaper after he's pooed, he says "ick,poo poo".
Here is a copy and paste of an article that was helpful to me in deciding when to toilet train:
<<One year (or sooner) is an average age for walking to begin. It is not considered developmentally sound to attempt potty training at this time for at least two important reasons.
First, your one year old is too young to consistently be aware of, much less control his or her bodily functions. She or he is too busy mastering the voluntary muscles involved in walking to even consider the nuances of controlling involuntary processes. It would be overloading your toddler's system to introduce an additional developmental challenge, especially one that he or she cannot be successful at achieving. This could cause delays in other areas of development that are primed for this time.
Secondly, an expectation to perform (even mildly) on the potty at this period in development could result in feelings of failure, inadequacy or general stress associated with toilet training. Early pressure could thwart the emotional sense of pride that coincides with successful toilet training later. Your child could miss out on the sense of mastery which is such a critical part of this developmental milestone when it occurs at the appropriate time.
Keep in mind that physical and emotional development are mutually occurring and influence each other. Natural stages of emotional and physical mastery build on each other and are best experienced sequentially in the naturally occurring readiness of the child. The natural period of time that consistent interest in toilet training occurs is usually between two and three years of age.
It is at this age that children have already mastered some sense of accomplishment from being able to successfully manipulate their environment in many ways. They can go get a toy for themselves, reach out to pet a cat, pull a book off a shelf, build a tower and use language to get what they want in the world. It is from this cumulative experience that the emergence of a separate, "confident" self emerges to master toilet training.
Self-regulation is a huge and prideful achievement because the child is aware of the accomplishment. Early toilet training often results in regression later on, which the child may experience as a sense of shame or failure, rather than pride and confidence.
Playing with the potty or observing others on the potty may prove interesting at one year of age. It may even serve as a kind of preparation for later toilet training, but it will not result in successful control of the release of complex sphincter muscles which are largely involuntary.
I am certain that your child will help you learn these things in a more concrete fashion than is explained here. Rest assured that parenting is not only instinctive, but learned from the feedback your child provides.>>