This is how my husband, the mathematician, always approaches these questions:
So, airfare is $1200
I'm guessing you'd spend $200 on gas
Flying would take what, 3 hours each way?
Driving will take 16 hours, each way
So you'll "spend" 26 hours of your life to save $1000. That's $38/hour. Does that seem like a reasonable price for your time?
Not a lot of people are "worth" more than $38/hour, so I think for many people, this is not crazy.
Personally, I'd be more inclined to do it if we were also able to extend the trip and find a nice halfway points to stop on each way and kind of make the journey part of the vacation. How long you get to stay also factors into my choice -- you say you'd leave on Friday and arrive on Saturday -- if this is a long weekend trip, then I'd be reluctant to give up 26 hours. If it's a week trip, then I'd be more willing.