Yes, please no lap sitting. It's not even likely to be allowed, and if it DID cause a problem for someone, it is a step in the direction of nobody being allowed to have pets in the cabin anymore.
My tips:
1. Make really, really sure you have ALL entry requirements for the animals for going to Japan.
2. Teach her how to pee/poop on command on a potty pad, so you can take her to the bathroom once or twice during the flight. Lay a potty pad down, let her go, then put her back in her carrier before returning to your seat. This will go much better if she knows to go on command, as it will be a strange place.
3. Make sure your carrier fits under the seat, where it will stay. A nice carrier is the Sleepypod Air which allows a lot of leg room while the plane is in the air.
I wouldn't be too concerned about the first flight, to FL. You've probably taken longer car trips.

But it is good practice for the process.