I think it depends on the breed; TBs are fast growers/maturers and I believe reach full height around 3/4 (they'll broaden out and continue maturing until they're 7) Cobs mature later but I'd be guessing if I said at what age they reach full height.
She is very young SJ and having read your previous post on riding lessons if you were to start owning one I would increase the lessons until you feel a bit more confident before you think about ownership. You would also be much better with an older horse that has done quite a bit.
Some people do begin training when a horse is 3 especially if they are pretty big but then tend to turn them away to grow up a bit. If this pony has done any work at all it will be limited, do you really want to begin by trying to break a pony?
There is a formula which you can take measurements & from that you can work out approcximate height a horse or pony will make at maturity...unfortunately I don't know the formula.