When my daughters became old enough to drive, they were required to get a job to pay the difference in insurance and put gas in the car. My parents required the same of me, plus I had to buy my own car. Nothing wrong with teaching some responsibility IMO. As far as the scooter goes, by the time you buy a decent scooter, the safety gear for it, and pay for service and upkeep, you will probably be spending at least as much as the increase in insurance, especially if you are looking at a 150cc.
Good luck....I was terrified when my daughters started driving. I turned gray overnight..LOL.