First of all, what do you mean by "mopeds?" Actual pedal mopeds, or small scooters? Do you need a certain speed to keep up with traffic? If you have steep hills, I don't recommend a small scooter, their CVT transmissions do not like hills. A 50cc 2 speed Tomos moped will easily outclimb my Vino 125, if you back off the throttle and let it stay in first gear. A small motorcycle, say 125cc, with a manual transmission will blow by a 125cc scooter like it was standing still going up a hill. The MadAss 125 should work if it is a manual transmission. If you seriously want something your kid can use as a dirt bike, then a small displacement dual sport is the way to go, just make sure the kid stays off the road with it. No 11 year old belongs on the road, though I was riding a dirt bike on rural country roads at that age.
2002 Vulcan 750 (engine out, slowly being disassembled) 2013 Royal Enfield B5
2001 XT225, 2009 Genuine Stella
2012 Zuma 125, 1980 Puch moped