Please don't belt the child to the operator. If the child isn't old enough to hang on for themselves don't ride them. The most secure position is for the child to have their strongest arm around the operator's waist and their other hand holding the grab rail. That way they are well-braced both directions. Alternately they can have both arms around the operator.
I get chills thinking about a spill where the two are tied together. Internal organ injuries, crushing injuries, etc.
Around the neighborhood, slow rides are a different animal. If your neighborhood is quiet (I've been up since 5:00 A.M. and haven't seen a single car, and I live on a corner) and the speed limit is 20 MPH (like most residential neighborhoods) then a toot around the block is probably O.K., with or without gear. Just don't do anything like demonstrate the acceleration, braking or turning capabilities. Just being on a motorcycle for the first time is plenty enough of a thrill. Oops, just saw the first car pass and it's 9:52 A.M.