Oh, I get ya. Well, to be honest, if it were me I would let the axle sit in the very top of the dropout and do the wheelnuts up tight. If a 15 stone bloke was going park riding on it then I'd say sort out the correct 'top hat' washers for the dropouts, but as its for a child it won't give you any concern as long as the nuts stay tight.
As for finding the right washers for the job, I'm not sure where you'll find them...