Can't resist, but children don't seem to need tickets in your part of the world.
Boy, 11, boards plane with no ticket
Maybe more helpfully I would say that a 3 year old will not enjoy a flight in a light aircraft - they can't see, it is noisy and they are far more prone to sickness.
Some open microlights may be more suitable (as he can see straight out), but I wouldn't take someone so young up unless they were known and VERY well behaved. Any planned flight should be very short, so that would keep costs down.
I still fondly remember trips to the airfield when I was that sort of age, so perhaps a special effort to be near the aircraft would be sufficient to keep the enthusiasm going.