How do I transfer my Minecraft account to my new PC and add a different account to the old PC?
Solution 1:
Minecraft accounts aren't connected to a PC. The launcher will helpfully remember your login for you, but this is only a convenience — your account isn't locked to it. You can just log in on your new PC and you will be able to play.
Your sister will need to have a new paid account. When she does, she can ignore your old account on the old PC and log in with her new account and be able to play.