The trip there
Kaylee spent last night in the ship. She wasn't about to let anything happen to it and was up way before anyone was due to arrive to run it through another check. She would have stayed in the engine room for the trip, been in constant contact with Wash and made sure that they got there safely. When it was time to see the judge, she would have once again stayed with the ship because she feels responsible for it and she knows that she's not very good at speaking especially not to people as important to the Earth's survival as the Celestials. Besides she's happiest with her ship anyway.