A few of caveats to that:

1) If your dream domicile has over a million people and your future airline has 25% or greater market share, consider making the move. If not, remember Cleveland, Dallas (Delta), Memphis, Nashville, Pittsburgh, Raleigh, Seattle, etc. were all crew bases majors either shut down or are currently starving out.

2) If you're at Alaska, American, Delta, or Southwest I'd think really hard before leaving for UAL once you're off first year pay.

3) I don't know when your dad retired, but UAL pilots in particular should understand you're just an employee/necessary expense and nothing more. Flying airliners isn't a higher calling and there's no loyalty. If necessary, they will put you on the street or declare bankruptcy. Make it a business decision on your end, because whomever you go to work for certainly understands that it is for them.

4) I've seen it work both ways. I've saw a pilot leave Alaska for American in '93 to be instantly furloughed for three years. I saw pilots leave US Air in '99 and TWA in 2000 for American, which both worked out. I guess the lesson there is if your carrier is financially stable, stay, if not, go.