Flying with Pets? Please help!!?

Me and my parents are moving to Scottsdale, Arizona. We live right now in Brighton, Mi. My dad got a job new job in Tempe so we are moving. But my question is i have 2 dog that are large size dogs (Lab, and Newfoundland) and 1 cat. We were thinking on bring the cat on with us and checking the dogs. Would it be safe and etc. (We would fly Northwest Airlines)