If I qualify for Alimony, and wish to leave the state does that mean my Alimony would stop.

If you are a recipient of life time alimony, maintenance or spousal support, your entitlement would not end because you left the state and in fact, you could enforce your order from any other state.  If, however, you are leaving the state to cohabit with an unrelated partner, or to take a job, it might have an impact.  If you have an agreement it should specify what circumstances would trigger a discontinuance of the alimony.  Please let me know if you have any questions.