Fly. For a shorter trip, under 10 hours, I might say drive because planes can be germy places and I don't know that I'd want to expose an 8 week old to all that. But 20 hours is a lot of hours. If your daughter is planning on nursing, that's frequent feedings and she wouldn't be able to take the baby out of the car seat to nurse while the car is moving so it would necessitate a stop to feed, and then change the resulting diaper.
If you do choose flying, I would recommend purchasing a seat for the infant and bringing along the car seat to use on the airplane. Make sure the car seat has a sticker stating it can be used for air travel. It's safer to have the baby buckled into a seat.