K.J.
I grew up in a very musical family and studied music in college, so I definitely understand and share your desire to encourage music with your little ones. Honestly, what you are doing now is great for his age.
Most instructors/musicians don't recommend starting children in formal or even regular lessons until they are about six years old...even older(sometime between 2nd and 5th grade). The reason is that, by then, the attention span of most children is more equal to the demands of learning the piano. Much of learning to read music and play the piano requires semi-advanced language and math skills. Understanding tempo and rhythm requires addition and division, and "theory" is literally music math.
As for now, encouraging free expression and familiarity with instruments is perfect and a good way to help your son develop an ear for melody and pitch recognition. Unless you are pushing for a child prodigy, just singing and encouraging involvement in music will help him develop on his own.
On the other hand, some start their children in music groups that help children recognize more of the formal elements of music (rhythm, pitch) in an informal environment around age four. I just moved to the area, so I am no help in recommendations, but I am sure there are other moms who would love to get together for a "music time" with their toddlers without paying a fee. I know I would! And, you already have such an advantage that you have a piano for experimenting and playing. I am definitely jealous. :)
Anyway, let me know if you find more interested moms or if you decide to do something on your own and I would be happy to talk more with you about it. Good luck with his creative mind! He sounds exceptionally bright for his age. :)