IF he is broke, at least to halter and lead, then you could enter him in a halter class or showmanship at halter. that wouldn't be a problem with his age.
then again, if he is broke and de-sensitized to all kinds of things, you could even enter him in fun shows/playdays. those are little shows that are huge competition things. we are having one in a couple of weeks where i live and it is just for fun and the experience of getting our horses around other horses and noises, etc.
there are plenty of 2 yr olds out there competing in all kinds of events!!!!! the older the better though, as it gives them a little more time to mature and get settled.
just check around your area, feed stores, tack shops, etc. there should be flyers put up there, that are announcing fun shows/playdays.