Copying CheckBook along with a backup over to an external drive should do the trick—you'll then be set for copying these two items to the new Mac, anytime later on. Just open the application, go to the File menu at the top of the screen, and select the Backup menu item, to save the backup (which will be an exact duplicate of your existing data file in its current state). Then, look for the application itself in your Applications folder.
In the end, you can simply double-click the copied-over backup to have it open in CheckBook on the new computer. At first launch, you'll just need to validate with your serial number—should you not have that on file, visit
https://splasm.com/support/premay2019or ... lookup.php , to retrieve it.