We got my son an Epiphone Les Paul Pee Wee as part of a kit when he was 4. He spent a fair amount of time trying to play it - it went out of tune like crazy - I don't know if it was due to the tuning heads, the short scale, or both, but he got so frustrated with the sound that he stopped. After he grew a little, say age 8-9, he started playing my full sized electrics, but couldn't handle a full sized dreadnought acoustic because he couldn't get his right (picking) arm around the body of the guitar. I bought him a parlor sized acoustic for his 10th birthday that he could play. Now he's 15 and bigger and is a really good player with no constraints on which guitar he can play.
I have to say, his playing had a lot more to do with his own drive to learn and play than it did with any particular guitar. Try to get a read on that (in retrospect, it was obvious even at age 4 with him) before you spend too much $.