Tony,
You will not neccesarily get cheaper car insurance if you tell your insurance company that you've changed jobs. It really depends on what type of job you were doing before and what your new job is about? For example, if you were working as an administrative clerk before and now you've become a sales guy who is always on the move, then you car insurance will go up because your previous job meant that your car was parked throughout the day and the chances of you getting involved in an accident were smaller while now you are always driving places and constantly on the road and at risk. You might be interested to know about other
factors which affects your car insurance and could potentially bring down your quote as well.
I'd give the insurance company a call if I was you and tell them about the new job and see if that makes a difference in the premiums to know for sure.