After some research, you might be able to export & import registry data, but it requires some work that can permanently damage your computer if you do stuff you shouldn't.
First, open the Registry editor by searching regedit in the Windows start menu:
Then, navigate to the Takodachi & Friends folder which is located in HKEY_CURRENT_USER\SOFTWARE\MonAmiral\Takodachi and friends:
If you left-click on the folder, you should see something similar to me: that's all the data that the game stores. You can then right-click and select Export:
Make sure to export only the selected items, not everything! It would be catastrophic to transfer all the data of your old computer to your new computer:
Save the file and transfer it so that you can use it after resetting your computer. Once everything is reset, double-click on the file and it will apply the changes, and the data should be transferred.
I have not tested this! If you want, you can send me the file and I will use it to see if it works.
Hope it helps!