Glad you're enjoying the game!
All settings/unlockables get stored in a file in your home directory:
~/.prefs/rs_data
You'll need to create a directory called ".prefs" in your new laptop's home directory, and from there you should just be able to copy the "rs_data" file over.
More info: https://libgdx.com/wiki/preferences#storage
Let us know if you need any other help transferring it over!