Razor MX350

Sure, it's not made by one of the Japanese Big Four.

And it's not gasoline powered.

But the Razor MX350 is a great first dirt-bike for a child.

Clutchless operation; chain drive.

Not street legal; no headlights or turn signals. 

Quiet operation; won't annoy the neighbors.

Nobby, tubeless tires.

Single, rear, drum brake.  The brake and throttle are interlocked; squeezing the brake lever turns off the throttle.