Morning Aviatn,
What is your reason for wanting to leave your current job?
Are you sure that is a good move at the moment?
I sure any airline would view you as a "non type rated" pilot, so you would end up completing a type conversion once you joined that company.
As for the right way to go about it, you will have to do what every other person is doing, networking etc. Or go to the middle east!
Good luck.