My advice to you is to contact first the unemployment office of your state of residence. States work together on exchanging information and they have rules as to which state pays for people in your situation. Thedude is correct in that most, if not all, states have a one week waiting period when you do not receive benefits. And be sure you read the requirements for staying eligible each and every week.

What I find appalling with your airline is the lack of support with the transition and short term career help. Most employers, at the minimum, will ask the unemployment office people (in Washington State, that department is the Department of Employment Security (ESD)) to give a group presentation covering everything from basic finances, resume help, job leads, interview tips, training/school, etc.

Quite honestly, I don't even want to know which airline you are flying for right now. Nauseating how airlines treat employees.