Your idea is very good. Although she has moved to a new house, you don't need to give her anything. You can send her a red envelope to congratulate her on moving after the move is completed. Otherwise, she is under too much pressure, which will affect the normal communication between you.

Second, I suggest that you help her when she moves. First, it can enhance your understanding, because moving requires communication and tacit cooperation. Second, show your physical quality and leave a good impression on her.

Third, if you have moved and you didn't help, you can use this as an excuse to ask her out to dinner to make up for your "fault" of not contributing.