We had to talk the instructor into taking our DD at 6, though he was quite pleased with how well she was picking things up. The teaching focused primarily on basic skills acquisition, though he did try to tailor it to our DD's interests in order to make it fun for her. For example, he asked her to bring in a CD of a song she liked, and after listening a bit, he translated part of it into something she could play.
Here are our lessons learned:
1) Instrument quality matters. The child will not practice if it's going to sound bad no matter what she does. That creates a problem... how much are you willing to spend on a hobby that your child, at this age, is very likely to set aside after three weeks? If you know enough about guitars that you can accurately diagnose most basic problems, no worries (which I guess you can, given that you said you studied privately starting at 8). Otherwise, I suggest you find someone who can to go with you to pick out an instrument.
2) Size matters. My DD set aside her guitar for months when she thought she couldn't play the top strings. In this case, the guitar was properly sized for her, and she just needed a grip adjustment. But what's the market like for guitars correctly sized for 2.5yos? And wouldn't they likely be of poor quality?
I like the ukelele solution suggested earlier. Otherwise, drums and keyboards are good for budding 2.5yo rockers. In your place, I'd let your DS know the guitar is in his future if he still wants it, once his hands grow into it.
