My son, now 5, has been flying with me regularly since he was 2. To start with I would always take another adult as well, so if he threw a wobbly (unusual) I didn't have to fly and deal with him at the same time. Since he was 4 I will fly with him alone, though I have made a vow not to do single pilot hard IFR with him... this following an attempt to speak to Shawbury, Gloucester and him at the same time...
He has the 'cadet' headset mentioned, and his own hi-viz jacket (try a riding supplier!) which he loves. He is now allowed to sit in the front, being old enough not to fiddle, and loves doing simple jobs like turning lights and fuel pump on and off on demand - next will be tuning radios, once he can reach them!
He uses a car 'booster' seat with the standard seatbelt. He still sleeps frequently - often on the return trip from somewhere - and usually wakes up only when the wheels touch down. Must be something about my landings!
A word of warning - he likes to help me with ground handling but last summer his foot was run over by a C152 and he broke two toes. He healed quickly - but it was a reminder that one can overestimate how much children can do/help. He dined out on that story for months, though. These days he mostly stands at a safe distance while I move the aircraft myself.
He does want to be a pilot... not helped by his godfather being a commercial pilot...
Tim