You can change jobs, should not be a problem (better pay is good), provided you are certain that the new job will (a) also be skilled, and (b) your employer will write that letter...

Yes, the job is the same as the one I have right now, same title, same environment, just a different company
I don't see why the wouldn't write me that letter. Unless I do something very wrong that would get me fire but that is nearly impossible as I need that experience to be eligible for CEC
I had a job before, but it wasn't skilled. I decided to walk out because problems I had with the manager, it wasn't worth staying there and I had not witnesses to prove what he was doing; I decide to leave without giving notice.
On my CEC application, they ask for work experience for the last 3 years and to provide a letter from every employer I had. What happens if I don't get a letter from that particular employer? I know it does not count for my skilled work experience, is just I job I had.
Should I try to get that letter anyways?
Thanks